Question

If (x-2) is a factor of x^3+4x^2+ax+b and x^3-ax^2+bx +8 then find the value of a and b

Answer 1

Answer:

Given,

x-2 is a factor of x³+ax²+bx+16

⇒2 is the zero of polynomial p(x)=x³+ax²+bx+16

⇒p(2)=(2)³+a(2)²+b(2)+16

⇒0=8+4a+2b+16

Given,b=4a

⇒0=8+4a+2(4a)+16

⇒0=8+12a+16

⇒12a= -24

⇒a=(-24)/12

⇒a= -2

b=4a

⇒b=4(-2)

⇒b= -8

value of a is -2 and b is -8

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