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Find the value of k for which the quadratic equation kx (x − 2) + 6 = 0 has two equal roots.

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#### Solution

Given quadratic equation is:

kx( x − 2 )+ 6 = 0

⇒ kx^{2 }− 2kx + 6 = 0

For a quadratic equation to have equal roots,

b^{2 }− 4ac = 0

Comparing the given equation with general equation ax^{2 }+ bx + c =0

We get a = k, b = −2k and c = 6

(−2k)^{2 }− 4(k)(6) = 0

⇒ 4k^{2 }− 24k = 0

⇒ 4k ( k − 6 ) = 0

Therefore, k = 0 and k = 6.

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