Question

If x = 0 and x= -1 are the zeroes of the polynomial f[x]=2X^3-3X^2+ax=b Then find the value of a and b.

Answer 1

Answer:

Let f(x)=ax^3+3x^2-13 and g(x)=2x^3-5x+a

given divisor =x-2

x-2=0=>x=2 (BY FACTORS THEOREM)

given when the polynomials are divided by x-2

we will get the same remainder let that be R

f(2)=a(2^3)+3(2^2)-13 and g(2)=2(2^3)-5(2)+a

=>a(8)+3(4)-13 and 2(8)-5(2)+a

=>8a-1=R.........(1) and a+6=R.........(2)

(1)-(2)

=>8a-1-a-6=R-R

=>7a-7=0

=>7a=7

=>a=7