find the value of k for which the quadratic equation (k-2)x^2 + 2(2k-3)x +(5k-6) = 0 has equal roots
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equal roots means discriminant of quadratic = 0 e.g, D = b² - 4ac = 0
{2(2k-3)}² - 4(5k -6)(k-2) = 0
4(4k² - 12k + 9) - 4(5k² - 16k + 12 ) = 0
(4k² - 5k² ) + (-12k + 16k) + (9 -12) = 0
-k² + 4k - 3 = 0
k² - 4k + 3 = 0
(k -1)(k -3) = 0
k = 1 and 3
{2(2k-3)}² - 4(5k -6)(k-2) = 0
4(4k² - 12k + 9) - 4(5k² - 16k + 12 ) = 0
(4k² - 5k² ) + (-12k + 16k) + (9 -12) = 0
-k² + 4k - 3 = 0
k² - 4k + 3 = 0
(k -1)(k -3) = 0
k = 1 and 3
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