Question

Ifx³+x² - ax + bis divisible by (x² - x), write the values of a and b.​

Answer 1

It is given that the polynomial f(x)=x3+x2−ax+b is divisible by x2−x which can be rewritten as x(x−1). It means that the given polynomial is divisible by both x and (x−1) that is they both are factors of f(x)=x3+x2−ax+b. 

Therefore, x=0 and x=1 are the zeroes of f(x) that is both f(0)=0 and f(1)=0.

Let us first substitute x=0 in f(x)=x3+x2−ax+b as follows:

f(0)=03+02−(a×0)+b⇒0=03+02−(a×0)+b⇒0=0+b⇒b=0

Now, substitute x=1:

f(1)=13+12−(a×1)+b⇒0=1+1−a+b⇒0=2−a+b⇒0=2−a+0

a=2