Question

Find the value of $k$ for which the equation
$x^2+kx+81=0$ and $x^2-6\sqrt{2}x+k=0$ has both real roots, $k>0$

• A. $k=9$
• B. $k=18$
• C. $k=3\sqrt{2}$
• D. No such value

Answer 1

The correct option is B $k=18$

For, $x^2+kx+81=0$ to have real roots

$k^2-324\ge 0$ $\Rightarrow$ $k\ge \mathrm{18.......}\left(1\right)$

For $x^2-6\sqrt{2}x+k=0$ to have real roots

$72-4k\ge 0$ $\Rightarrow$ $k\le \mathrm{18..........}\left(2\right)$

For both equations to have real roots $k=18$