Question

For what value of $k$ are the roots of the quadratic equation $3x^2+2kx+27=0$ real and equal?

Answer 1

$\Rightarrow$ The given equation $3x^2+2kx+27=0$

Here, $a=3,b=2k,c=27$

It is given that roots are real and equal.

$\therefore$ $b^2-4ac=0$

$\Rightarrow$ $(2k{)}^2-4(3\left)\right(27)=0$

$\Rightarrow$ $4k^2-324=0$

$\Rightarrow$ $4k^2=324$

$\Rightarrow$ $k^2=81$

$\therefore$ $k=\pm 9$