Question

The value of xthe value of x cube + x square minus x is equal to 10 if ​

Answer 1

Answer:

It is given that the polynomial f(x)=x

3

+x

2

−ax+b is divisible by x

2

−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)=x

3

+x

2

−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)=x

3

+x

2

−ax+b as follows:

f(0)=0

3

+0

2

−(a×0)+b

⇒0=0

3

+0

2

−(a×0)+b

⇒0=0+b

⇒b=0

Now, substitute x=1:

f(1)=1

3

+1

2

−(a×1)+b

⇒0=1+1−a+b

⇒0=2−a+b

⇒0=2−a+0(∵b=0)

⇒a=2

Hence, a=2 and b=0.