Question

If $\alpha ,\beta$ are the zeros of the polynomial $x^2$ - px + 36 and ${\alpha }^2$+${\beta }^2$ = 9, then what is the value of p?

• A. ±6
• B. ±3
• C. ±8
• D. ±9

Answer 1

The correct option is D

±9

Here a = 1, b = -p, c = 36.

$\alpha +\beta =\frac{-b}{a}=p$

$\alpha \beta =\frac{c}{a}=36$


${\alpha }^2$+${\beta }^2={(\alpha +\beta )}^2$ - 2$\alpha \beta$

$\Rightarrow$ $p^2-2\times 36=9$

$\Rightarrow$$p^2=81$

$\Rightarrow p=9$ or $-9$