Find the value of $k$ for which the equation $2 x^{2} - k x + 3 = 0$ will have two real and equal roots.

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Solution

Given the equation is $2 x^{2} - k x + 3 = 0$ .

The discriminant of this equation $= b^{2} - 4 a c = (- k)^{2} - 4 \times 2. \times 3 = k^{2} - 24.$

Since the roots of the quadratic equation are all real and equal then the discriminant will be zero.

Then we've,

$k^{2} - 24 = 0$

or, $k^{2} = 24$

or, $k = \pm 2 \sqrt{6}$ .

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