Question

Find the values of k such that the quadratic equation x^2-2kx+(7k-12)=0 has real and equal roots.
Someone solve it for me, with steps.

Answer 1

★ QUADRATICS RESOLUTION ★

☣ FOR EQUAL ROOTS , D=0 , b² = 4ac

☣ GIVEN EQUATION → x² -2kx + (7k - 12 ) = 0

☣ APPLYING THE PRECONDITION ...

☣ 4K² = 4 [ 7K - 12 ]

☣ 4K² = 28K - 48

☣ 4K² - 28K + 48 =0

☣ K² - 7K + 12 = 0

☣ K² - 4K -3K + 12 = 0

☣ K² - 3K - 4K + 12 = 0

☣ K ( K - 3 ) - 4 ( K - 3 ) = 0

☣ [K - 4] [ K - 3] = 0

☣ HENCE ...

☣ K = 4 , 3 ARE THE REQUIRED VALUES OF "K"

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