Question

If the equation x²+2(k+2)x+9k=0 has equal roots then the value of k will be? *1 or 4

-1 or 4

1 or -4

-1 or -4

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Answer 1

Answer:

Discriminant = 0

$(2k + 4) {}^{2} - 4 \times 1 \times 9k = 0$

$4 {k}^{2} + 16k + 16 - 36k = 0$

$4 {k}^{2} - 20k + 16 = 0$

${k}^{2} - 5k + 4 = 0$

${k}^{2} - 4k - k + 4 = 0$

$k(k - 4) - 1(k - 4) = 0$

$(k - 4)(k - 1) = 0$

$k = 1 \: \: or \: \: 4$