The quadratic equation whose roots are the numbers having arithmetic mean 34 and geometric mean 16 is
The quadratic equation whose roots are the numbers having arithmetic mean 34 and geometric mean 16 is
$x^{2}+68 x-256=0$
$x^{2}-68 x-256=0$
$x^{2}-68 x+256=0$
$x^{2}+68 x+256=0$
Solution
Quad $E q^{n}: \rightarrow$
$A M \text { of } a, b=34$
$a+b=68$
GM of $a, b,=\pm 6$
$\begin{aligned} a, b \rightarrow \text { roots } \rightarrow \quad a b &=256 \\ x^{2}-68 x+256 &=0 \end{aligned}$