Question

If $4$ and $-3$ are the zeros of the polynomial $2x^2-px+4$ and $q{x}^3-3x+2p$, then $p+q$ is:

• A. $8$
• B. $9$
• C. $10$
• D. $11$

Answer 1

The correct option is C $10$

Given,
$4$ is the zero of the polynomial $2x^2-px+4$.
$⟹2(4{)}^2-4p+4=0$
$⟹32-4p+4=0$
$⟹36-4p=0$
$⟹4p=36$
$⟹p=\frac{36}{4}=9$

Also, $-3$ is the zero of the polynomial $q{x}^3-3x+2p$
$⟹q(-3{)}^3-3(-3)+2\times 9=0$ (Because $p=9$)
$⟹-27q+9+18=0$
$⟹-27q+27=0$
$⟹27q=27$
$⟹q=\frac{27}{27}=1$

$p+q=9+1=10$