If 9x^2 + 3px + 6q when divided by (3x + 1) leaves a remainder (-3/4) -Maths 9th

If 9x^2 + 3px + 6q when divided by (3x + 1) leaves a remainder (-3/4) -Maths 9th
by

1 Answer

Answer :

Given, (9x2 + 3px + 6q), when divided by (3x + 1) leaves a remainder −34−34 ∴ f(x) = 9x2 + 3px + 6q – (−34)(−34) = (9x2+3px+6q+34)(9x2+3px+6q+34) is exactly divisible by (3x + 1)  ∴ f(−34)(−34) = 0 ⇒ 9(−34)(−34)2 + 3 p . (−34)(−34) + 6q + 3434 = 0 ⇒ 6q - p + 7474 0  ⇒ 24q - 4p + 7 = 0                      ......(i) Now, the expression g(x) = qx2 + 4px + 7 is exactly divisible by x + 1  ⇒ g(–1) = 0 ⇒ q – 4p + 7 = 0                     ...(ii)  Solving equations (i) and (ii), we get q = 0, p = 7474.
by

Related questions

Find the remainder when f(x)=9x(cube) -x 3x(square) + 14x - 3 is divided by g(x)=(3x-1). -Maths 9th

Description : Find the remainder when f(x)=9x(cube) -x 3x(square) + 14x - 3 is divided by g(x)=(3x-1). -Maths 9th

Last Answer : Solution :-

If x^5 – 9x^2 + 12x – 14 is divisible by (x – 3), what is the remainder ? -Maths 9th

Description : If x^5 – 9x^2 + 12x – 14 is divisible by (x – 3), what is the remainder ? -Maths 9th

Last Answer : answer:

If the expressions (px^3 + 3x^2 – 3) and (2x^3 – 5x + p) when divided by (x – 4) leave the same remainder, then what is the value of p ? -Maths 9th

Description : If the expressions (px^3 + 3x^2 – 3) and (2x^3 – 5x + p) when divided by (x – 4) leave the same remainder, then what is the value of p ? -Maths 9th

Last Answer : Given that the following polynomials leave the same remainder when divided by (x - 4) : We are to find the value of a. Remainder theorem: When (x - b) divides a polynomial p(x), then the remainder is p(b). So, from (i) and (ii), we get Thus, the required value of a is 1.

If the polynomials ax^3 + 4x^2 + 3x – 4 and x^3 – 4x + a leave the same remainder when divided by (x – 3), the value of a is : -Maths 9th

Description : If the polynomials ax^3 + 4x^2 + 3x – 4 and x^3 – 4x + a leave the same remainder when divided by (x – 3), the value of a is : -Maths 9th

Last Answer : Given ax^3 + 4x^2 + 3x - 4 and x^3 - 4x + a leave the same remainder when divided by x - 3. Let p(x) = ax^3 + 4x^2 + 3x - 4 and g(x) = x^3 - 4x + a By remainder theorem, if f(x) is divided by (x − a) then ... 4 27a+41 g(3)=27-4(3)+a 15+a f(3)=G(3) 27a+41=15+a 26a=15-41 a=15-41/26 a=-26/26 a=-1

What should be subtracted from 27x^3 – 9x^2 – 6x – 5 to make it exactly divisible by (3x – 1) -Maths 9th

Description : What should be subtracted from 27x^3 – 9x^2 – 6x – 5 to make it exactly divisible by (3x – 1) -Maths 9th

Last Answer : answer:

The polynomial p{x = x4 -2x3 + 3x2 -ax+3a-7 when divided by x+1 leaves the remainder 19. -Maths 9th

Description : The polynomial p{x = x4 -2x3 + 3x2 -ax+3a-7 when divided by x+1 leaves the remainder 19. -Maths 9th

Last Answer : p(x) is divided by x+ 2 =

The polynomial p{x = x4 -2x3 + 3x2 -ax+3a-7 when divided by x+1 leaves the remainder 19. -Maths 9th

Description : The polynomial p{x = x4 -2x3 + 3x2 -ax+3a-7 when divided by x+1 leaves the remainder 19. -Maths 9th

Last Answer : p(x) is divided by x+ 2 =

If x^3 + 5x^2 + 10k leaves remainder – 2x when divided by x^2 + 2, then what is the value of k ? -Maths 9th

Description : If x^3 + 5x^2 + 10k leaves remainder – 2x when divided by x^2 + 2, then what is the value of k ? -Maths 9th

Last Answer : x3+5x2+10k =(x2+2)(x+5)+10k−2x−10 ⇒10k−2x−10=−2x ⇒10k−10=0 or k=1.

If the expression ax^2 + bx + c is equal to 4, when x = 0, leaves a remainder 4 when divided by x + 1 and leaves a -Maths 9th

Description : If the expression ax^2 + bx + c is equal to 4, when x = 0, leaves a remainder 4 when divided by x + 1 and leaves a -Maths 9th

Last Answer : Given exp. f(x) = ax2 + bx + c ∴ When x = 0, a.0 + b.0 + c = 4 ⇒ c = 4. The remainders when f(x) is divided by (x + 1) and (x + 2) respectively are f(–1) and f(–2). ∴ f( ... 2b = 2 ...(ii) Solving (i) and (ii) simultaneously we get, a = 1, b = 1.

If ax^3 + bx^2 + x – 6 has (x + 2) as a factor and leaves a remainder 4, when divided by (x – 2), the value of a and b respectively are : -Maths 9th

Description : If ax^3 + bx^2 + x – 6 has (x + 2) as a factor and leaves a remainder 4, when divided by (x – 2), the value of a and b respectively are : -Maths 9th

Last Answer : Let p(x) = ax³ + bx² + x - 6 A/C to question, (x + 2) is the factor of p(x) , and we know this is possible only when p(-2) = 0 So, p(2) = a(-2)³ + b(-2)² - 2 - 6 = 0 ⇒ ... --(2) solve equations (1) and (2), 4a = 0 ⇒a = 0 and b = 2 Then, equation will be 2x² + x - 6

Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Description : Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Last Answer : Remainder = 145 Again, we should evaluate p(5) Let p(y) = y3 + y2 - 2y + 5 ∴ p(5) = 53 + 52 - 2 x 5 + 5 = 125 + 25 - 10 + 5 = 145 Thus , we find that p(5) is the remainder when p(y) is divided by y - 5 .

Determine the remainder when polynomial p(x) is divided by x - 2 . -Maths 9th

Description : Determine the remainder when polynomial p(x) is divided by x - 2 . -Maths 9th

Last Answer : p(x) = x4 - 3x2 + 2x - 5 According to remainder theorem, the required remainder will be = p(2) p(x) = x4 - 3x2 + 2x - 5 ∴ p(2) = 24 - 3(2)2 + 2(2) - 5 =16 - 12 + 4 - 5 = 3

If x51 + 51 is divided by x + 1, then the remainder is -Maths 9th

Description : If x51 + 51 is divided by x + 1, then the remainder is -Maths 9th

Last Answer : (d) Let p(x) = x51 + 51 . …(i) When we divide p(x) by x+1, we get the remainder p(-1) On putting x= -1 in Eq. (i), we get p(-1) = (-1)51 + 51 = -1 + 51 = 50 Hence, the remainder is 50.

By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial x4 + 1 and x-1. -Maths 9th

Description : By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial x4 + 1 and x-1. -Maths 9th

Last Answer : Actual division method

By remainder theorem, find the remainder when p(x) is divided by g(x) -Maths 9th

Description : By remainder theorem, find the remainder when p(x) is divided by g(x) -Maths 9th

Last Answer : Find the remainder when p(x) is divided by g(x)

If the polynomials az3 +4z2 + 3z-4 and z3-4z + 0 leave the same remainder when divided by z – 3, -Maths 9th

Description : If the polynomials az3 +4z2 + 3z-4 and z3-4z + 0 leave the same remainder when divided by z – 3, -Maths 9th

Last Answer : Let p1(z) = az3 +4z2 + 3z-4 and p2(z) = z3-4z + o When we divide p1(z) by z - 3, then we get the remainder p,(3). Now, p1(3) = a(3)3 + 4(3)2 + 3(3) - 4 = 27a+ 36+ 9-4= 27a+ 41 When we ... to' the question, both the remainders are same. p1(3)= p2(3) 27a+41 = 15+a 27a-a = 15 - 41 . 26a = 26 a = -1

Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Description : Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Last Answer : Remainder = 145 Again, we should evaluate p(5) Let p(y) = y3 + y2 - 2y + 5 ∴ p(5) = 53 + 52 - 2 x 5 + 5 = 125 + 25 - 10 + 5 = 145 Thus , we find that p(5) is the remainder when p(y) is divided by y - 5 .

Determine the remainder when polynomial p(x) is divided by x - 2 . -Maths 9th

Description : Determine the remainder when polynomial p(x) is divided by x - 2 . -Maths 9th

Last Answer : p(x) = x4 - 3x2 + 2x - 5 According to remainder theorem, the required remainder will be = p(2) p(x) = x4 - 3x2 + 2x - 5 ∴ p(2) = 24 - 3(2)2 + 2(2) - 5 =16 - 12 + 4 - 5 = 3

If x51 + 51 is divided by x + 1, then the remainder is -Maths 9th

Description : If x51 + 51 is divided by x + 1, then the remainder is -Maths 9th

Last Answer : (d) Let p(x) = x51 + 51 . …(i) When we divide p(x) by x+1, we get the remainder p(-1) On putting x= -1 in Eq. (i), we get p(-1) = (-1)51 + 51 = -1 + 51 = 50 Hence, the remainder is 50.

By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial x4 + 1 and x-1. -Maths 9th

Description : By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial x4 + 1 and x-1. -Maths 9th

Last Answer : Actual division method

By remainder theorem, find the remainder when p(x) is divided by g(x) -Maths 9th

Description : By remainder theorem, find the remainder when p(x) is divided by g(x) -Maths 9th

Last Answer : Find the remainder when p(x) is divided by g(x)

If the polynomials az3 +4z2 + 3z-4 and z3-4z + 0 leave the same remainder when divided by z – 3, -Maths 9th

Description : If the polynomials az3 +4z2 + 3z-4 and z3-4z + 0 leave the same remainder when divided by z – 3, -Maths 9th

Last Answer : Let p1(z) = az3 +4z2 + 3z-4 and p2(z) = z3-4z + o When we divide p1(z) by z - 3, then we get the remainder p,(3). Now, p1(3) = a(3)3 + 4(3)2 + 3(3) - 4 = 27a+ 36+ 9-4= 27a+ 41 When we ... to' the question, both the remainders are same. p1(3)= p2(3) 27a+41 = 15+a 27a-a = 15 - 41 . 26a = 26 a = -1

If x to the power 11 + 101 is divided by x+1,what is the remainder? -Maths 9th

Description : If x to the power 11 + 101 is divided by x+1,what is the remainder? -Maths 9th

Last Answer : Solution :-

Find the remainder when f(x)=4x(cube) - 12x(square) +14x - 3 is divided by g(x) = (2x-1). -Maths 9th

Description : Find the remainder when f(x)=4x(cube) - 12x(square) +14x - 3 is divided by g(x) = (2x-1). -Maths 9th

Last Answer : ____2x2-5x+4________________ 2x-1 ) 4x3-12x2+14x-3( 4x3-2x2 - + ____________ 0 -10x2+14x-3 ... + ___________ X+1

If the polynomials az3 + 42z2 + 3z – 4 and z3 - 4z + a leave the same remainder when divided by z – 3, find the value of a. -Maths 9th

Description : If the polynomials az3 + 42z2 + 3z – 4 and z3 - 4z + a leave the same remainder when divided by z – 3, find the value of a. -Maths 9th

Last Answer : Solution :-

When x^13 + 1 is divided by x –1, the remainder is : -Maths 9th

Description : When x^13 + 1 is divided by x –1, the remainder is : -Maths 9th

Last Answer : answer:

When (x^3 – 2x^2 + px – q) is divided by (x^2 – 2x – 3), the remainder is (x – 6), What are the values of p and q respectively ? -Maths 9th

Description : When (x^3 – 2x^2 + px – q) is divided by (x^2 – 2x – 3), the remainder is (x – 6), What are the values of p and q respectively ? -Maths 9th

Last Answer : answer:

When a + b + c + 3a^(1/3) b^(2/3) + 3a(2/3) b^(1/3) is divided by a^(1/3) + b^(1/3) + c^(1/3), what is the remainder ? -Maths 9th

Description : When a + b + c + 3a^(1/3) b^(2/3) + 3a(2/3) b^(1/3) is divided by a^(1/3) + b^(1/3) + c^(1/3), what is the remainder ? -Maths 9th

Last Answer : answer:

When x^40 + 2 is divided by x^4 + 1, what is the remainder ? -Maths 9th

Description : When x^40 + 2 is divided by x^4 + 1, what is the remainder ? -Maths 9th

Last Answer : answer:

If the remainder of the polynomial a0 + a1x + a2x^2 + ....... + anx^n when divided by (x – 1) is 1, then which one of the following is correct ? -Maths 9th

Description : If the remainder of the polynomial a0 + a1x + a2x^2 + ....... + anx^n when divided by (x – 1) is 1, then which one of the following is correct ? -Maths 9th

Last Answer : answer:

The remainder when 1 + x + x^2 + x^3 + ........ + x^(1007) is divided by (x – 1) is -Maths 9th

Description : The remainder when 1 + x + x^2 + x^3 + ........ + x^(1007) is divided by (x – 1) is -Maths 9th

Last Answer : answer:

If the polynomial x^19 + x^17 + x^13 + x^11 + x^7 + x^5 + x^3 is divided by (x^2 + 1), then the remainder is : -Maths 9th

Description : If the polynomial x^19 + x^17 + x^13 + x^11 + x^7 + x^5 + x^3 is divided by (x^2 + 1), then the remainder is : -Maths 9th

Last Answer : answer:

When a polynomial f(x) is divided by (x – 3) and (x + 6), the respective remainders are 7 and 22. What is the remainder when f(x) is -Maths 9th

Description : When a polynomial f(x) is divided by (x – 3) and (x + 6), the respective remainders are 7 and 22. What is the remainder when f(x) is -Maths 9th

Last Answer : answer:

The remainder, when x^(200) is divided by x^2 – 3^x + 2 is -Maths 9th

Description : The remainder, when x^(200) is divided by x^2 – 3^x + 2 is -Maths 9th

Last Answer : answer:

When x^3 + 2x^2 + 4x + b is divided by (x + 1), the quotient is x^2 + ax + 3 and the remainder -Maths 9th

Description : When x^3 + 2x^2 + 4x + b is divided by (x + 1), the quotient is x^2 + ax + 3 and the remainder -Maths 9th

Last Answer : answer:

Factorise : x2 + 9x +18 -Maths 9th

Description : Factorise : x2 + 9x +18 -Maths 9th

Last Answer : Factorisation

Factorise : x2 + 9x +18 -Maths 9th

Description : Factorise : x2 + 9x +18 -Maths 9th

Last Answer : Factorisation

Check whether polynomial p(x) = 2x(cube) - 9x(square) + x + 12 is a multiple of 2x-3 or not. -Maths 9th

Description : Check whether polynomial p(x) = 2x(cube) - 9x(square) + x + 12 is a multiple of 2x-3 or not. -Maths 9th

Last Answer : Solution :-

Factorise (9x -1/5)2 - (x + 1/3)2. -Maths 9th

Description : Factorise (9x -1/5)2 - (x + 1/3)2. -Maths 9th

Last Answer : Solution :-

Factorise (9x-1/5)^2 + (x+1/3)^2 -Maths 9th

Description : Factorise (9x-1/5)^2 + (x+1/3)^2 -Maths 9th

Last Answer : This answer was deleted by our moderators...

Evaluate x if log3 (3 + x) + log3 (8 – x) – log3 (9x – 8) = 2 – log39 -Maths 9th

Description : Evaluate x if log3 (3 + x) + log3 (8 – x) – log3 (9x – 8) = 2 – log39 -Maths 9th

Last Answer : (c) 4log3 (3 + x) + log3 (8 - x) - log3 (9x - 8) = 2 - log39 ⇒ log3 (3 + x) + log3 (8 - x) - log3 (9x - 8) + log39 = 2⇒ log3 \(\bigg[rac{(3+x)(8-x)(9)}{(9x-8)}\bigg]=2\)⇒ \(rac{9(24+8x-3x-x^2)}{(9x- ... = 9x - 8 ⇒ x2 + 4x - 32 = 0 ⇒ (x + 8) (x - 4) = 0 ⇒ x = - 8, 4. Taking the positive value x = 4.

If (x + 1) is a factor of x^4 + 9x^3 + 7x^2 + 9ax + 5a^2, then : -Maths 9th

Description : If (x + 1) is a factor of x^4 + 9x^3 + 7x^2 + 9ax + 5a^2, then : -Maths 9th

Last Answer : answer:

Find the perpendicular distance between the lines 9x + 40y – 20 = 0 and 9x + 40y + 21 = 0. -Maths 9th

Description : Find the perpendicular distance between the lines 9x + 40y – 20 = 0 and 9x + 40y + 21 = 0. -Maths 9th

Last Answer : Given line: x - 2y = 3 ⇒ y = \(rac{x}{2}\) - \(rac{3}{2}\) ....(i)∴ Its slope = m1 = \(rac{1}{2}\)Let m2 be the slope of line through (3, 2). Since this line is inclined at 45º to line (i),tan 45º = \(\bigg ... (x -3)⇒ 3y - 6 = - x + 3 or y - 2 = 3x - 9 ⇒ 3y + x - 9 = 0 or y - 3x + 7 = 0.

f(x) = x^4 – 2x^3 + 3x^2 – ax + b is a polynomial such that when it is divided by (x – 1) and (x + 1), the remainders are respectively 5 and 19. -Maths 9th

Description : f(x) = x^4 – 2x^3 + 3x^2 – ax + b is a polynomial such that when it is divided by (x – 1) and (x + 1), the remainders are respectively 5 and 19. -Maths 9th

Last Answer : answer:

Evaluate: `lim_(x rarr oo) (x^(5)+3x^(4)-4x^(3)-3x^(2)+2x+1)/(2x^(5)+4x^(2)-9x+16)`.

Description : Evaluate: `lim_(x rarr oo) (x^(5)+3x^(4)-4x^(3)-3x^(2)+2x+1)/(2x^(5)+4x^(2)-9x+16)`.

Last Answer : Evaluate: `lim_(x rarr oo) (x^(5)+3x^(4)-4x^(3)-3x^(2)+2x+1)/(2x^(5)+4x^(2)-9x+16)`.

Find the values of x for which the following functions are maximum or minimum: (i) ` x^(3)- 3x^(2) - 9x ` (ii) ` 4x^(3)-15x^(2)+12x+1` (iii) ` 1-x-x^(

Description : Find the values of x for which the following functions are maximum or minimum: (i) ` x^(3)- 3x^(2) - 9x ` (ii) ` 4x^(3)-15x^(2)+12x+1` (iii) ` 1-x-x^(

Last Answer : Find the values of x for which the following functions are maximum or minimum: (i) ` x^(3)- 3x^(2) - 9x ` (ii) ` 4x ... (v) `(x^(2)-x+1)/(x^(2)+x+1)`

How do you simplify 3x-9x?

Description : How do you simplify 3x-9x?

Last Answer : 12

9x-3x squared?

Description : 9x-3x squared?

Last Answer : 12

2. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. -Maths 10th

Description : 2. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. -Maths 10th

Last Answer : Let a be any positive integer and b = 6. Then, by Euclid’s algorithm, a = 6q + r, for some integer q ≥ 0, and r = 0, 1, 2, 3, 4, 5, because 0≤r

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. -Maths 10th

Description : Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. -Maths 10th

Last Answer : Let a' be any positive integer and b = 6. ∴ By Euclid's division algorithm, we have a = bq + r, 0 ≤ r ≤ b a = 6q + r, 0 ≤ r ≤ b [ ∵ b = 6] where q ≥ 0 and r = 0,1, 2, 3, 4, ... numbers. Therefore, any odd integer can be expressed is of the form 6q + 1, or 6q + 3, or 6q + 5 where q is some integer