When f(x) = x4 - 2x3 + 3x2 - ax is divided by x + 1 and x - 1 , we get remainders as 19 and 5 respectively . -Maths 9th

When f(x) = x4 - 2x3 + 3x2 - ax is divided by x + 1 and x - 1 , we get remainders as 19 and 5 respectively . -Maths 9th
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When f(x) is divided by (x+1) and (x-1) , the remainders are 19 and 5 respectively .  ∴ f(-1) = 19 and f(1) = 5 ⇒ (-1)4 - 2 (-1)3  + 3(-1)2 - a (-1) + b = 19  ⇒ 1 +2 + 3 + a + b = 19 ∴ a + b = 13 ------- (i) Again , f(1) = 5 ⇒ 14 - 2 × 13 + 3 × 12 - a × 1 b = 5 ⇒ 1 - 2 + 3 - a + b = 5 ∴ b - a = 3 ------ (ii) solving eqn (i) and (ii) , we get  a = 5 and b = 8 Now substituting the values of a and b in f(x) , we get   ∴ f(x) = x4 - 2x3 + 3x2 - 5x + 8 Now f(x) is divided by (x-3) so remainder will be f(3)   ∴ f(x) =  ∴ f(x) = x4 - 2x3 + 3x2 - 5x + 8 ⇒ f(3) = 34 - 2 × 33 + 3 × 32 - 5 × 3 + 8  = 81 - 54 + 27 - 15 + 8 = 47    
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When f(x) = x4 - 2x3 + 3x2 - ax is divided by x + 1 and x - 1 , we get remainders as 19 and 5 respectively . -Maths 9th

Description : When f(x) = x4 - 2x3 + 3x2 - ax is divided by x + 1 and x - 1 , we get remainders as 19 and 5 respectively . -Maths 9th

Last Answer : When f(x) is divided by (x+1) and (x-1) , the remainders are 19 and 5 respectively . ∴ f(-1) = 19 and f(1) = 5 ⇒ (-1)4 - 2 (-1)3 + 3(-1)2 - a (-1) + b = 19 ⇒ 1 +2 + 3 + a + b = 19 ∴ a + b = 13 ------- ... + 3x2 - 5x + 8 ⇒ f(3) = 34 - 2 33 + 3 32 - 5 3 + 8 = 81 - 54 + 27 - 15 + 8 = 47

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

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

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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

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Let R1 and R2 be the remainders when the polynomials x^3 + 2x^2 – 5ax – 7 and x^2 + ax^2 – 12x + 6 are divided by (x + 1) and (x – 2) respectively. -Maths 9th

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x4+3x3+3x2+x+1 -Maths 9th

Description : x4+3x3+3x2+x+1 -Maths 9th

Last Answer : Solution: Let p(x)= x4+3x3+3x2+x+1 The zero of x+1 is -1. p(−1)=(−1)4+3(−1)3+3(−1)2+(−1)+1 =1−3+3−1+1 =1 ≠ 0 ∴By factor theorem, x+1 is not a factor of x4+3x3+3x2+x+1

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Factorise: 2x3 - 3x2 - 17x + 30. -Maths 9th

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