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

Solution

## 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, $$b^2-4ac=0$$$$(-k)^2-4(2)(k)=0$$$$k^2-8k=0$$$$k(k-8)=0$$$$\therefore$$  $$k=0$$ and $$k=8$$$$\therefore$$  Values of $$k$$ are $$0,\,8$$Mathematics

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