Find the values of *k* for each of the following quadratic equations, so that they have two equal roots.

kx (x - 2) + 6 = 0

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#### Solution

kx(x - 2) + 6 = 0

or kx^{2} - 2kx + 6 = 0

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

a = k, b = - 2k and c = 6

Discriminant = b^{2} - 4ac

= ( - 2k)^{2} - 4 (k) (6)

= 4k^{2} - 24k

For equal roots,

b^{2} - 4ac = 0

4k^{2} - 24k = 0

4k (k - 6) = 0

Either 4k = 0 or k = 6 = 0

k = 0 or k = 6

However, if k = 0, then the equation will not have the terms 'x^{2}' and 'x'.

Therefore, if this equation has two equal roots, k should be 6 only

Concept: Nature of Roots

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