Question

If $2$ zero's of a cubic polynomial are $0$, then it has no first degree or constant terms.

• A. True
• B. False

Answer 1

The correct option is A (True)

Consider the cubic polynomial $a{x}^3+b{x}^2+cx+d$.
Then, $\alpha \beta +\beta \gamma +\gamma \alpha =\frac{c}{a}$, ....(i)
$\alpha \beta \gamma =-\frac{d}{a}$.......(ii)
Given, $\alpha ,\beta =0$ as any two zero's are $0$.
then from equation (i), $c=0$ and from equation(ii) $d=0$.
$\alpha +\beta +\gamma =-\frac{b}{a}⟹$ "b" is not zero. Since, one of the roots is not equal to zero.
Since, $c=0$, and $d=0$ the polynomial does not have first degree or constant terms.