Question

3. Find the value of 'a' if the polynomials ax3 4x2 + 3x -4 and x-4x+ a leave the same remainder when divided by (X-3)​

Answer 1

Answer:

Mark as a brilliant please

Step-by-step explanation:

Let p(x) = ax3 + 4x2 + 3x - 4 and q(x) = x3 - 4x + a be the given polynomials.

When p(x) and q(x) are divided by (x - 3) the remainder are p(3) and q(3) respectively.

p(3) = q(3) given

a(3)3 + 4(3)2 + 3 x 3 - 4 = 33 - 4 x 3 + a

a(3)3 + 4(3)2 + 3 x 3 - 4 = 33 - 4 x 3 + a⇒ 27a + 36 + 9 - 4 = 27 - 12 + a

a(3)3 + 4(3)2 + 3 x 3 - 4 = 33 - 4 x 3 + a⇒ 27a + 36 + 9 - 4 = 27 - 12 + a⇒ 26a = 15 - 41

a(3)3 + 4(3)2 + 3 x 3 - 4 = 33 - 4 x 3 + a⇒ 27a + 36 + 9 - 4 = 27 - 12 + a⇒ 26a = 15 - 41⇒ 26a = -26

a(3)3 + 4(3)2 + 3 x 3 - 4 = 33 - 4 x 3 + a⇒ 27a + 36 + 9 - 4 = 27 - 12 + a⇒ 26a = 15 - 41⇒ 26a = -26∴ a =

a(3)3 + 4(3)2 + 3 x 3 - 4 = 33 - 4 x 3 + a⇒ 27a + 36 + 9 - 4 = 27 - 12 + a⇒ 26a = 15 - 41⇒ 26a = -26∴ a =-2626

= -1.