Question

Find the value of k in order that 2x3
– 9x2
+ x + k may be exactly divisible by ( 2x – 3)

Answer 1

Answer:

Given that, 2x+3 is a factor of the polynomial p(x)=2x3+9x2−x−b

According to the factor theorem, if (x−a) is a factor of f(x), then f(a)=0.

Therefore, by Factor theorem p(−23)=0

⇒2(−23)3+9(−23)2−(−23)−b=0

⇒−427+481+23−b=0

⇒4−27+81+6−b=0⇒b=460=15

∴ b=15