Question

write a polynomial function in standard form with zeros -1,1 and 0

Answer 1

The polynomial having zeros 1, -1, 0 can be written as

$f(x)=k(x-0)(x-1)(x-(-1))$ where k is a real number

$\implies\,f(x)=kx(x-1)(x+1)$

Using

$\boxed{\bf\,(a+b)(a-b)=a^2-b^2}$

$\implies\,f(x)=kx(x^2-1)$

$\implies\,f(x)=k(x^3-x)$

$\therefore\text{The required polynomial is }\bf\,f(x)=k(x^3-x)$

Find more:

Obtain all the zeros of the polynomial 3x^3+10x^2-9x-4 if one of its zero is 1

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