Q2.    Find the values of k for each of the following quadratic equations, so that they have two equal roots.                (ii)    $kx(x-2) + 6 = 0$

D Divya Prakash Singh

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

The value of the discriminant $D= 0$.

Given equation: $kx(x-2) + 6 = 0$

Can be written as: $kx^2-2kx+6 = 0$

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

$a = k, \ b = -2k,\ c = 6$

The value of $D = b^2-4ac = (-2k)^2 - 4(k)(6) = 0$

$\Rightarrow 4k^2 - 24k = 0$

$\Rightarrow 4k(k-6) = 0$

$\Rightarrow k= 0\ or\ 6$

But $k= 0$ is NOT possible because it will not satisfy the given equation.

Hence the only value of $k$ is 6 to get two equal roots.

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