Question

29. If the polynomials ax3 + 4x2 + 3x – 4 and x3 – 4x + a leave the same remainder when
divided by x - 3, find the value of a.
OR

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Given :-

The polynomials ax3 + 4x2 + 3x – 4 and x3 – 4x + a leave the same remainder when divided by x - 3

To Find :-

The value of a

Solution :-

Polynomials Given :

Let p(x) = ax³ + 4x² + 3x – 4

And q(x) = x³ – 4x + a

According to the Question

p(3) = q(3)  

a(3)3 + 4(3)2 + 3 × 3 – 4 = 33 – 4 × 3 + a

⇒  27a + 36 + 9 – 4 = 27 – 12 + a

⇒ 26a = 15 – 41

⇒ 26a = - 26

⇒ a = - 26/26

⇒ a = -1

Hence, the required value of a 1.