Question

For what positive values of k, does the quadratic equation $3x^2-kx+3=0$ not have equal roots?

Answer 1

For equal roots, discriminant should be zero.

Given equation: $3x^2-kx+3=0$

Compare above equation with general form $a{x}^2+bx+c=0$ , we get

$a=3,b=-k,c=3$

So discriminant, $D=b^2-4ac=0$
$\Rightarrow b^2-4ac=0$
$\Rightarrow k^2-4\left(3\right)\left(3\right)=0$
$\Rightarrow k^2=36$
$\Rightarrow k=6$ or $-6$

Since, we have to find only positive value of $k$

Hence, value of $k$ is $6$