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Values of k for which the quadratic equation $2 x^{2} + kx + k = 0$ has equal roots

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4,8

0,4

4,-8

0,8

answer is D.

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Detailed Solution

We have been given a quadratic equation

2 x^{2} + kx + k = 0

.
We have to find the value of k for the quadratic equation to have equal roots.
Now, we know that the given equation is of the form

a x^{2} + bx + c = 0

and to have equal roots the value of the discriminant of an equation will be equal to zero.
So, we have given the question that equation

2 x^{2} + kx + k = 0

has equal roots.
So, we have D=0
Now, we know that D=

\sqrt{b^{2} - 4 ac}

Now, substituting the values we get
⇒

\sqrt{b^{2} - 4 ac}

=0
⇒

\sqrt{k^{2} - 4 \times 2 \times k}

=0
⇒

\sqrt{k^{2} - 8 \times k}

=0
⇒

k^{2} - 8

k=0 ⇒k(k−8)=0
Or we can write k=0 and k−8=0
So, we get two values of k, k=0 and k=8.
Option 4 is the correct answer.

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Values of k for which the quadratic equation 2x2+kx+k=0 has equal roots

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Values of k for which the quadratic equation $2 x^{2} + kx + k = 0$ has equal roots