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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

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

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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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