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  4. The value of k (k > 0) for which the equation x2 + kx + 64 = 0 and x2 - 8x + k = 0 both will have real roots, is

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Q. The value of $k (k > 0)$ for which the equation $x^2 + kx + 64 = 0$ and $x^2 - 8x + k = 0$ both will have real roots, is

Complex Numbers and Quadratic Equations

Solution:

Since $x^2 + Kx + 64 = 0$,
$x^2 - 8x + K = 0$ have real roots,
$\therefore \, K^2 - 256 \geq 0$ and $64 - 4 K \geq 0$
$\Rightarrow \, K^2 \geq \, 256 $ and $16 \geq K$
$\therefore \, K = 16 \, [\because \, K > 0] $