Question

Q) If the polynomial ax³+3x²-13 and 2x³-5x+a leaves the same remainder when divided by ( x - 2) find the value of a.​

Answer 1

Answer:

Hey your answer is there☝️☝️

Answer 2

$\huge\b{Answer:}}$

Given : If the polynomials ax³ + 3x² - 13 and 2x³ - 5x + a when divided by (x - 2) leave the same remainder.

 

Let p (x) = ax³ + 3x² - 13 and q (x) = 2x³ - 5x + a  be the given polynomials. The remainders when p(x) and q(x) are divided by (x - 2) are p (2) and q (2) .

By the given condition, we have :

p(2) = q(2)

⇒ a (2)³ + 3(2)² – 13 = 2 (2)³ – 5(2) + a

⇒ a × 8 + 3 × 4 – 13 = 2 × 8  – 5(2) + a

⇒ 8a + 12 – 13 = 16 – 10 + a

⇒ 8a - 1 = 6 + a

⇒ 8a - a = 6 + 1

⇒ 7a = 7

⇒ 7a = 7

⇒ a = 7/7

⇒ a = 1

Hence, the value of 'a' is 1.