Question

plz help me people..very imp..tomorrow is my exam..

Answer 1

for an equation to have equal roots discriminant of equation should zero.
$( - 2(1 + 3k)) {}^{2} - 4 (7(2k + 3)) = 0 \\ 4(1 + 3k) {}^{2} = 4 \times 7 \times (2k + 3) \\ (1 + 3k) {}^{2} = 7(2k + 3) \\ 1 + 9 {k}^{2} + 6k = 14k + 21 \\ 9k {}^{2} - 20 - 8k = 0 \\ 9k {}^{2} - 8k - 20 = 0 \\ so \: k \: = 2 \\ opt(2)$

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