If the roots of the equation x^2 - (3k - 1)x | vedclass

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Question

(C) For a quadratic equation $ax^2 + bx + c = 0$ to have equal roots,the discriminant $D = b^2 - 4ac$ must be equal to $0$.
Here,$a = 1$,$b = -(3k -

Vedclass · Accepted Answer

Both $A$ and $B$

Vedclass · Answer

(C) For a quadratic equation $ax^2 + bx + c = 0$ to have equal roots,the discriminant $D = b^2 - 4ac$ must be equal to $0$.
Here,$a = 1$,$b = -(3k - 1)$,and $c = 2k^2 + 2k$.
Setting the discriminant to zero:
$D = [-(3k - 1)]^2 - 4(1)(2k^2 + 2k) = 0$
$(3k - 1)^2 - 4(2k^2 + 2k) = 0$
$9k^2 - 6k + 1 - 8k^2 - 8k = 0$
$k^2 - 14k + 1 = 0$
Using the quadratic formula $k = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$:
$k = \frac{14 \pm \sqrt{(-14)^2 - 4(1)(1)}}{2(1)}$
$k = \frac{14 \pm \sqrt{196 - 4}}{2} = \frac{14 \pm \sqrt{192}}{2} = \frac{14 \pm 8\sqrt{3}}{2} = 7 \pm 4\sqrt{3}$.

If the roots of the equation $x^2 - (3k - 1)x + 2k^2 + 2k = 0$ are equal,then the value of $k$ will be .....

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