Question

Which of the following sets contain all roots of the polynomial

Answer 1

All these given roots are contained in option C.

The given equation is :

$9x^{3}+9x^{2}-4x-4=0$

$9x^{2}(x+1)-4(x+1)=0$

$(9x^{2}-4)(x+1)=0$

$9x^{2}-4=0,x+1=0$

$x^{2}=\frac{4}{9},x=-1$

$x=\frac{2}{3},x=-1$

Roots = $-1,\frac{-2}{3} ,\frac{2}{3}$

Hence these lie in between $(\frac{-3}{2} ,\frac{3}{2})$