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Question

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


A
0 only
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B
4
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C
8 only
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D
0,8
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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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