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Question

If the equation x2-2x(1+3k)+7(3+2k)=0 has equal roots, then k = ?
(a) 2 or 109
(b) -2 or 109
(c) 2 or -109
(d) -2 or -109

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Solution

(c) 2 or -109

It is given that the roots of the equation (x2 2x(1 + 3k) + 7(3 + 2k) = 0 are equal. (b2 4ac) = 0 {2(1 + 3k)}2 4 × 1 × 7(3 + 2k) = 0 4(9k2 + 6k + 1) 28(3 + 2k) = 0 36k2 + 24k + 4 84 56k = 0 36k2 32k 80 = 0 9k2 8k 20 = 0 9k2 18k + 10k 20 = 0 9k(k 2) + 10(k 2) = 0 (k 2)(9k + 10) = 0 k = 2 or k = 109

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