Question

If the equation in x, $x^4+p{x}^3+q{x}^2$ = 16(2x – 1), where p, q $ϵ$ R has all positive roots and A.M. of roots = H.M. of roots, then

• A. q : |p| = 3 : 2
• B. p > 8
• C. $q\ge 4$
• D. p < 0 < q < 8

Answer 1

The correct option is C

$q\ge 4$

A.M. of roots = H.M. of roots
$\Rightarrow \alpha =\beta =\gamma =\delta =2\left(each\right)$
Where $\alpha ,\beta ,\gamma ,\delta$ are roots of given equation
$\therefore$ p =-8, q = 24