Question

THE POLYNOMIAL (ax^3+3x^2-3)and(2x^3-5x+a)when divided by (x-4)leave the same remainder .FIND THE VALUE​


if any one will answer I will mark him or her brainliest plzz answer fast

Answer 1

Answer:

a = 1

Step-by-step explanation:

Let p(x) = ax³ + 3x² - 3 and g(x) = 2x³ - 5x + a

Put x - 4 = 0 or x = 4 in p(x) and g(x).

p(4) = a(4)³ + 3(4)² - 3

      = 64a + 48 - 3

      = 64a + 45

g(4) = 2(4)³ - 5(4) + a

      = 128 - 20 + a

      = 108 + a

Now,

p(x) and g(x) leaves the same remainder.

⇒ 64a + 45 = 108 + a

⇒ 63a = 63

⇒ a = 1

Therefore, the value of a = 1

Hope it helps!

Answer 2

Since given equations result in the same remainder when divided by (x-4), set f(4)1=f(4)2.

f(4)1=ax^3 + 3x^2 - 3=64a+48-3

f(4)2=2x^3 - 5x + a=128-20+a

64a+48-3=128-20+a

63a=63

a=1