Question

if x-2 and x+3 are factors of ax^3+3x^2-bx-12 find the value of a and b​

Answer 1

Answer:

a=1

b=4

Step-by-step explanation:

x-2=0

x=2

f(x)=a*2*2*2+3*2*2-b*2-12=0 (given x-2 is a factor)

8a+12-2b-12=0

8a-2b=0

dividing the equation by 2

4a-b=0----------(i)

x+3=0

x=-3

f(x)=a*(-3)*(-3)*(-3)+3*(-3)*(-3)-b*(-3)-12=0 (given x+3 is a factor)

-27a+27+3b-12=0

27a-3b-15=0

dividing the equation by 3

9a-b-5=0

9a-b=5----------(ii)

Simultaneously solving equations (i) and (ii)

Subtracting equation (i) from equation (ii)

9a-b=5

-4a+b=0

This implies that 5a= 5

Therefore a=1

4a-b=0 (equation (i))

4*1-b=0

b=4

Answer: a=1,b=4