Advertisements
Advertisements
Question
Find ‘a’ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Advertisements
Solution
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
The given polynomials are ax3 + 3x2 – 9
and 2x3 + 4x + a
Let p(x) = ax3 + 3x2 – 9
and q(x) = 2x3 + 4x + a
Given that p(x) and q(x) leave the same
remainder when divided by (x + 3),
Thus by Remainder Theorem, we have
p(–3) = q(–3)
⇒ a(–3)3 + 3(–3)2 - 9 = 2(–3)3 + 4(–3) + a
⇒ –27a + 27 – 9 = –54 – 12 + a
⇒ –27a + 18 = –66 + a
⇒ –27a - a = –66 – 18
⇒ -28a = –84
⇒ a = `(84)/(28)`
∴ a = 3.
APPEARS IN
RELATED QUESTIONS
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
Use Remainder theorem to factorize the following polynomial:
`2x^3 + 3x^2 - 9x - 10`
When x3 + 2x2 – kx + 4 is divided by x – 2, the remainder is k. Find the value of constant k.
Find ‘a‘ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leave the same remainder when divided by x + 3.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(2x3 − 2x2 + ax − a) ; (x − a)
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + 2
When a polynomial f(x) is divided by (x – 1), the remainder is 5 and when it is,, divided by (x – 2), the remainder is 7. Find – the remainder when it is divided by (x – 1) (x – 2).
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 3x2 + 4x + 50, g(x) = x – 3
4x2 – kx + 5 leaves a remainder 2 when divided by x – 1. The value of k is ______.
