Question

Find the value of a, if the polynomials ax 3 + 3x 2 – 3 and 2x 2 – 5x + a when divided by x– 4, leave the same remainder.

Answer 1

Answer:

Answer:The answer is -11/21. Hope it helps.

Answer:The answer is -11/21. Hope it helps.Mark me brainliest. Follow me.

Answer 2

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Find the value of a, if the polynomials ax 3 + 3x 2 – 3 and 2x 2 – 5x + a when divided by x– 4, leave the same remainder..

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$\boxed{\red{\bold{Given:}}}$

$p(x) = ax^3 + 3x^2 -3$

$f(x) = 2x^2 - 5x + a$

$g(x) = x-4$

$x- 4 = 0 \implies x = 4$

$\boxed{\red{\bold{Finding \ remainders \ 1:}}}$

$p(x) = ax^3 + 3x^2 -3$

$p(4) = a(4)^3 + 3(4)^2 - 3$

$p(4) = 64a + 48 - 3$

$p(4) = 64a + 45$

$R_1 = 64a + 45$

$\boxed{\red{\bold{Finding \ remainder \ 2:}}}$

$f(x) = 2x^2 - 5x + a$

$f(4) = 2(4)^2 - 5(4) + a$

$f(4) = 32 - 20 + a$

$f(4) = 12 + a$

$R_2 = 12 + a$

$\boxed{\red{\bold{Given \ relation:}}}$

$R_1 = R_2$

$64a + 45 = 12 + a$

$63 a = - 33$

$a = \displaystyle\frac{-11}{21}$

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