# Q2.    Find the values of k for each of the following quadratic equations, so that they have two equal roots.                (i)    $2x^2 + kx + 3 = 0$

D Divya Prakash Singh

For two equal roots for the quadratic equation: $ax^2+bx+c =0$

The value of discriminant $D= 0$.

Given equation: $2x^2 + kx + 3 = 0$

Comparing and getting the values of a,b, and, c.

$a = 2, \ b = k,\ c = 3$

The value of $D = b^2-4ac = (k)^2 - 4(2)(3)$

$\Rightarrow (k)^2 = 24$

Or, $\Rightarrow k=\pm \sqrt{24} = \pm 2\sqrt{6}$

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