Find the zeroes of the polynomial in each of the following, -Maths 9th

Find the zeroes of the polynomial in each of the following, -Maths 9th
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Answer :

(i) Given, polynomial is p(x) = x- 4 For zero of polynomial, put p(x) = x-4 = 0 ⇒  x= 4 Hence, zero of polynomial is 4. (ii) Given, polynomial is g(x) = 3-6x For zero of polynomial, put g(x) = 0 3 - 6x = 0 ⇒  6x =3 ⇒  x=1/2. Hence, zero of polynomial is X (iii) Given, polynomial is q(x) = 2x -7 For zero of polynomial, put q(x) =  2x-7 = 0 2x= 7 ⇒  x =7/2 Hence, zero of polynomial is (iv) Given polynomial h(y) = 2 y For zero of polynomial, put h(y) = 0 2y= 0 Hence, the zero of polynomial is 0,
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Find the zeroes of the polynomial in each of the following, -Maths 9th

Description : Find the zeroes of the polynomial in each of the following, -Maths 9th

Last Answer : (i) Given, polynomial is p(x) = x- 4 For zero of polynomial, put p(x) = x-4 = 0 ⇒ x= 4 Hence, zero of polynomial is 4. (ii) Given, polynomial is g(x) = 3-6x For zero of polynomial, put g(x) ... polynomial h(y) = 2 y For zero of polynomial, put h(y) = 0 2y= 0 Hence, the zero of polynomial is 0,

One of the zeroes of the polynomial 2x2 + 7x – 4 is -Maths 9th

Description : One of the zeroes of the polynomial 2x2 + 7x – 4 is -Maths 9th

Last Answer : (b) Let p (x) = 2x2 + 7x-4 = 2x2 + 8x-x-4 [by splitting middle term] = 2x(x+ 4)-1(x+ 4) = (2x-1)(x+ 4) For zeroes of p(x), put p(x) = 0 ⇒ (2x -1) (x + 4) = 0 ⇒ 2x-1 = 0 and x+4 = 0 ⇒ x = 1/2 and x = -4 Hence, one of the zeroes of the polynomial p(x) is 1/2.

Find the zeroes of the polynomial p(x)= (x – 2)2 – (x+ 2)2. -Maths 9th

Description : Find the zeroes of the polynomial p(x)= (x – 2)2 – (x+ 2)2. -Maths 9th

Last Answer : Given, polynomial is p(x) = (x – 2)2 – (x+ 2)2 For zeroes of polynomial, put p(x) = 0 (x – 2)2 – (x+ 2)2 = 0 (x-2 + x+2)(x-2-x-2) = 0 [using identity, a2-b2 =(a-b)(a + b)] ⇒ (2x)(-4) = 0

One of the zeroes of the polynomial 2x2 + 7x – 4 is -Maths 9th

Description : One of the zeroes of the polynomial 2x2 + 7x – 4 is -Maths 9th

Last Answer : (b) Let p (x) = 2x2 + 7x-4 = 2x2 + 8x-x-4 [by splitting middle term] = 2x(x+ 4)-1(x+ 4) = (2x-1)(x+ 4) For zeroes of p(x), put p(x) = 0 ⇒ (2x -1) (x + 4) = 0 ⇒ 2x-1 = 0 and x+4 = 0 ⇒ x = 1/2 and x = -4 Hence, one of the zeroes of the polynomial p(x) is 1/2.

Find the zeroes of the polynomial p(x)= (x – 2)2 – (x+ 2)2. -Maths 9th

Description : Find the zeroes of the polynomial p(x)= (x – 2)2 – (x+ 2)2. -Maths 9th

Last Answer : Given, polynomial is p(x) = (x – 2)2 – (x+ 2)2 For zeroes of polynomial, put p(x) = 0 (x – 2)2 – (x+ 2)2 = 0 (x-2 + x+2)(x-2-x-2) = 0 [using identity, a2-b2 =(a-b)(a + b)] ⇒ (2x)(-4) = 0

If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k. -Maths 9th

Description : If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k. -Maths 9th

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If the sum of zeroes of the quadratic polynomial 3x2 – kx + 6 is 3, then find the value of k. -Maths 9th

Description : If the sum of zeroes of the quadratic polynomial 3x2 – kx + 6 is 3, then find the value of k. -Maths 9th

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Is polynomial y4 + 4y2 + 5 have zeroes or not? -Maths 10th

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If ̳α ‘ and ̳β ‘ are the zeroes of a quadratic polynomial x 2 − 5x + b and α − β = 1, then the value of ̳b‘ is (a) – 5 (b) 6 (c) 5 (d) – 6

Description : If ̳α ‘ and ̳β ‘ are the zeroes of a quadratic polynomial x 2 − 5x + b and α − β = 1, then the value of ̳b‘ is (a) – 5 (b) 6 (c) 5 (d) – 6

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Description : How many zeroes does a linear equation have ?? -Maths 9th

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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

Which one of the following is a polynomial ? -Maths 9th

Description : Which one of the following is a polynomial ? -Maths 9th

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Description : Degree of the polynomial 4x4 + Ox3 + Ox5 + 5x+ 7 is -Maths 9th

Last Answer : (a) Degree of 4x4 + Ox3 + Ox5 + 5x + 7 is equal to the highest power of variable x. Here, the highest power of x is 4, Hence, the degree of a polynomial is 4.

Degree of the zero polynomial is -Maths 9th

Description : Degree of the zero polynomial is -Maths 9th

Last Answer : (d) The degree of zero polynomial is not defined, because in zero polynomial, the coefficient of any variable is zero i.e., Ox2 or Ox5,etc. Hence, we cannot exactly determine the degree of variable.

The value of the polynomial 5x – 4x2 + 3, when x = -1 is -Maths 9th

Description : The value of the polynomial 5x – 4x2 + 3, when x = -1 is -Maths 9th

Last Answer : (a) Let p (x) = 5x – 4x2 + 3 …(i) On putting x = -1 in Eq. (i), we get p(-1) = 5(-1) -4(-1)2 + 3= - 5 - 4 + 3 = -6

Zero of the zero polynomial is -Maths 9th

Description : Zero of the zero polynomial is -Maths 9th

Last Answer : (c) Zero of the zero polynomial is any real number. e.g., Let us consider zero polynomial be 0(x-k), where k is a real number For determining the zero, put x-k = 0 ⇒ x = k Hence, zero of the zero polynomial be any real number.

Zero of the polynomial p(x)=2x+5 is -Maths 9th

Description : Zero of the polynomial p(x)=2x+5 is -Maths 9th

Last Answer : (b) Given, p(x) = 2x+5 For zero of the polynomial, put p(x) = 0 ∴ 2x + 5 = 0 ⇒ -5/2 Hence, zero of the polynomial p(x) is -5/2.

If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is -Maths 9th

Description : If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is -Maths 9th

Last Answer : (c) Let p(x) = 2x2 + kx Since, (x + 1) is a factor of p(x), then p(-1)=0 2(-1)2 + k(-1) = 0 ⇒ 2-k = 0 ⇒ k= 2 Hence, the value of k is 2.

x + 1 is a factor of the polynomial -Maths 9th

Description : x + 1 is a factor of the polynomial -Maths 9th

Last Answer : (b) Let assume (x + 1) is a factor of x3 + x2 + x+1. So, x = -1 is zero of x3 + x2 + x+1 (-1)3 + (-1)2 + (-1) + 1 = 0 ⇒ -1+1-1 + 1 = 0 ⇒ 0 = 0 Hence, our assumption is true.

Give an example of a polynomial, which is -Maths 9th

Description : Give an example of a polynomial, which is -Maths 9th

Last Answer : (i) The example of monomial of degree 1 is 5y or 10x. (ii) The example of binomial of degree 20 is 6x20 + x11 or x20 +1 (iii) The example of trinomial of degree 2 is x2 – 5x+ 4 or 2x2 -x-1

Find the value of the polynomial 3x3 – 4x2 + 7x – 5, when x = 3 and also when x = -3. -Maths 9th

Description : Find the value of the polynomial 3x3 – 4x2 + 7x – 5, when x = 3 and also when x = -3. -Maths 9th

Last Answer : Let p(x) =3x3 – 4x2 + 7x – 5 At x= 3, p(3) = 3(3)3 – 4(3)2 + 7(3) – 5 = 3×27-4×9 + 21-5 = 81-36+21-5 P( 3) =61 At x = -3, p(-3)= 3(-3)3 – 4(-3)2 + 7(-3)- 5 = 3(-27)-4×9-21-5 = -81-36-21-5 = -143 p(-3) = -143 Hence, the value of the given polynomial at x = 3 and x = -3 are 61 and -143, respectively.

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

Determine which of the following polynomial has x – 2 a factor -Maths 9th

Description : Determine which of the following polynomial has x – 2 a factor -Maths 9th

Last Answer : first option is the correct answer for the given question solution is as follows:- let x-2=0 then, x=2 put x in (i) 3(2)(2)+6(2)-24=0 12+12-24=0 {use BODMAS rule for solution}... 24-24=0 0=0 this verifies our 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 =

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

Which one of the following is a polynomial ? -Maths 9th

Description : Which one of the following is a polynomial ? -Maths 9th

Last Answer : Following is a Polynomial

Degree of the polynomial 4x4 + Ox3 + Ox5 + 5x+ 7 is -Maths 9th

Description : Degree of the polynomial 4x4 + Ox3 + Ox5 + 5x+ 7 is -Maths 9th

Last Answer : (a) Degree of 4x4 + Ox3 + Ox5 + 5x + 7 is equal to the highest power of variable x. Here, the highest power of x is 4, Hence, the degree of a polynomial is 4.

Degree of the zero polynomial is -Maths 9th

Description : Degree of the zero polynomial is -Maths 9th

Last Answer : (d) The degree of zero polynomial is not defined, because in zero polynomial, the coefficient of any variable is zero i.e., Ox2 or Ox5,etc. Hence, we cannot exactly determine the degree of variable.

The value of the polynomial 5x – 4x2 + 3, when x = -1 is -Maths 9th

Description : The value of the polynomial 5x – 4x2 + 3, when x = -1 is -Maths 9th

Last Answer : (a) Let p (x) = 5x – 4x2 + 3 …(i) On putting x = -1 in Eq. (i), we get p(-1) = 5(-1) -4(-1)2 + 3= - 5 - 4 + 3 = -6

Zero of the zero polynomial is -Maths 9th

Description : Zero of the zero polynomial is -Maths 9th

Last Answer : (c) Zero of the zero polynomial is any real number. e.g., Let us consider zero polynomial be 0(x-k), where k is a real number For determining the zero, put x-k = 0 ⇒ x = k Hence, zero of the zero polynomial be any real number.

Zero of the polynomial p(x)=2x+5 is -Maths 9th

Description : Zero of the polynomial p(x)=2x+5 is -Maths 9th

Last Answer : (b) Given, p(x) = 2x+5 For zero of the polynomial, put p(x) = 0 ∴ 2x + 5 = 0 ⇒ -5/2 Hence, zero of the polynomial p(x) is -5/2.

If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is -Maths 9th

Description : If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is -Maths 9th

Last Answer : (c) Let p(x) = 2x2 + kx Since, (x + 1) is a factor of p(x), then p(-1)=0 2(-1)2 + k(-1) = 0 ⇒ 2-k = 0 ⇒ k= 2 Hence, the value of k is 2.

x + 1 is a factor of the polynomial -Maths 9th

Description : x + 1 is a factor of the polynomial -Maths 9th

Last Answer : (b) Let assume (x + 1) is a factor of x3 + x2 + x+1. So, x = -1 is zero of x3 + x2 + x+1 (-1)3 + (-1)2 + (-1) + 1 = 0 ⇒ -1+1-1 + 1 = 0 ⇒ 0 = 0 Hence, our assumption is true.

Give an example of a polynomial, which is -Maths 9th

Description : Give an example of a polynomial, which is -Maths 9th

Last Answer : (i) The example of monomial of degree 1 is 5y or 10x. (ii) The example of binomial of degree 20 is 6x20 + x11 or x20 +1 (iii) The example of trinomial of degree 2 is x2 – 5x+ 4 or 2x2 -x-1

Find the value of the polynomial 3x3 – 4x2 + 7x – 5, when x = 3 and also when x = -3. -Maths 9th

Description : Find the value of the polynomial 3x3 – 4x2 + 7x – 5, when x = 3 and also when x = -3. -Maths 9th

Last Answer : Let p(x) =3x3 – 4x2 + 7x – 5 At x= 3, p(3) = 3(3)3 – 4(3)2 + 7(3) – 5 = 3×27-4×9 + 21-5 = 81-36+21-5 P( 3) =61 At x = -3, p(-3)= 3(-3)3 – 4(-3)2 + 7(-3)- 5 = 3(-27)-4×9-21-5 = -81-36-21-5 = -143 p(-3) = -143 Hence, the value of the given polynomial at x = 3 and x = -3 are 61 and -143, respectively.

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

Determine which of the following polynomial has x – 2 a factor -Maths 9th

Description : Determine which of the following polynomial has x – 2 a factor -Maths 9th

Last Answer : first option is the correct answer for the given question solution is as follows:- let x-2=0 then, x=2 put x in (i) 3(2)(2)+6(2)-24=0 12+12-24=0 {use BODMAS rule for solution}... 24-24=0 0=0 this verifies our 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 =

FOR THE POLYNOMIAL -Maths 9th

Description : FOR THE POLYNOMIAL -Maths 9th

Last Answer : NEED ANSWER

FOR WHAT VALUE OF K, THE POLYNOMIAL X2+(4-K)X+2 IS DIVISIBLE BY X-2 -Maths 9th

Description : FOR WHAT VALUE OF K, THE POLYNOMIAL X2+(4-K)X+2 IS DIVISIBLE BY X-2 -Maths 9th

Last Answer : As the given polynomial divisible by x-2 means the polynomial satisfies for the value x=2 So putting x=2 in x²+(4-k)x+2 yields 0 ⇒2²+(4-k)2+2=0 ⇒4+8-2k+2=0 ⇒ 2k=14 ⇒ k= ... ;-3x+2 if factorized yields (x-1)(x-2). Thus is divisible by x-2 as well as divisible by x-1.