Question

If the polynomial ax³ + 3x² -13 and 2x³ – 5x + a when divided by (x – 2) leave the same remainder, find the Value of a

Answer 1

Answer:

a= 1

Step-by-step explanation:

f(x) = ax³ + 3x² -13

x-2=0, x=2

When we substitute x=2 in f(x)

f(2)=a(2)^3 + 3(2)^2 -13 = 8a + 12 - 13 = 8a - 1

g(x)= 2x³ – 5x + a

X=2

g(2)= 2(2)^3 - 5(2) + a = 16 - 10 + a = 6 + a

Since it is given that when the equations are divided by (x-2) they leave the same remainder,hence we can equate the remainders of the two equations.

8a-1 = 6 + a

8a-a = 6+1

7a= 7

a=1

Hope it helps!