Question

Find the positive value of k for which quadratic equation $x^2-8x+k=0$ have real roots?

Answer 1

The quadratic will have real root only when its discriminant will be greater than or equal to $0$

Discriminant of given equation $=b^2-4ac$ $={(-8)}^2-4\times 1\times k>0$

$\Rightarrow 64-4k>0$

$\Rightarrow 4k<64$

$\Rightarrow k<16$

So, the value of $k$ should be less than $16$.