Find the values of *k* for each of the following quadratic equations, so that they have two equal roots. 2*x*^{2} + *kx* + 3 = 0

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#### Solution

2x^{2} + kx + 3 = 0

Comparing equation with ax^{2} + bx + c = 0, we get

a = 2, b = k and c = 3

Discriminant = b^{2} - 4ac = (k)^{2} - 4(2) (3)

= k^{2} - 24

For equal roots,

Discriminant = 0

k^{2} - 24 = 0

k^{2} = 24

k = `±sqrt24 = ±2sqrt6`

Concept: Nature of Roots

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