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The polynomial p(x) = ax cube …

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The polynomial p(x) = ax cube + 4x square +3x-4 and g(x) = x cube - 4x +a leave the same remainder when divided by (x-3). Find the value of 'a'. Find the remainder when p(x) is divided by (x-).

Posted by Abhishek Patel 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Let p(x) = ax³ + 4x² + 3x - 4 and q(x) = x³ - 4x + a be the given polynomials. The remainders when p(x) and q(x) are divided by (x - 3) are p(3) and q(3) respectively.
By the given condition, we have
p(3) = q(3)
{tex}\Rightarrow{/tex} a {tex}\times{/tex}3³ + 4 {tex}\times{/tex}3² + 3 {tex}\times{/tex}3 - 4 = 3³ - 4 {tex}\times{/tex}3 + a
{tex}\Rightarrow{/tex} 27a + 36 + 9 - 4 = 27 - 12 + a
{tex}\Rightarrow{/tex} 26a + 26 = 0 {tex}\Rightarrow{/tex} 26a = -26 {tex}\Rightarrow{/tex} a = -1

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