Question

Values of k for which the quadratic equation $2x^2-kx+k=0$ has equal roots is?

• A. $0$ only
• B. $4$
• C. $8$ only
• D. $0,8$

Answer 1

The correct option is D $0,8$

$\Rightarrow$ The given quadratic equation is $2x^2-kx+k=0$

$\Rightarrow$ If the equation has equal roots, then the discriminant $b^2-4ac=0.$

$\Rightarrow$ Here, $a=2,b=-k,c=k$

Then, $b^2-4ac=0$

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

$k^2-8k=0$

$k(k-8)=0$

$\therefore$ $k=0$ and $k=8$

$\therefore$ Values of $k$ are $0,8$