Question

Find the value of k such that the quadratic equation x² - 2kx + (7k-12) =0 has equal roots.

Answer 1

Here is the answer☝☝

when a quadratic equation has equal roots its discriminant is equal to zero


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Answer 2

Hope u like my process
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For a quadratic equation with equal roots,

=> x² - 2ax + a² =0_____(1)
.. Be the formula.

So,

Comparing x² - 2kx +(7k-12) = 0 with equation (1) we get

$= > {k}^{2} = (7k - 12) \\ \\ or. \: \: {k}^{2} - 7x + 12 = 0 \\ \\ or. \: \: {k}^{2} - 4x - 3x + 12 = 0 \\ \\ or. \: \: k(k - 4) - 3(k - 4) = 0 \\ \\ or. \: \: (k - 3)(k - 4) = 0 \\ \\ \bf \underline{either} \\ \\ = > k - 3 = 0 \\ \\ or. \: \: \bf k = 3 \\ \\ \bf \underline{or} \\ \\ = > k - 4 = 0 \\ \\ or. \: \bf \: k = 4$


So, k = 3,4

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