Question

Determine the value(s) of m for which the equation
x? + m(4x + m - 1) + 2 = 0 has real roots.​

Answer 1

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Answer 2

$\bigstar \bf \: answer \\ \\ x {}^{2} + 4mx + (m {}^{2} - m + 2) = 0 \\ since \: d = 0 \\ d = b {}^{2} = 4ac \\ = (4m) {}^{2} - 4(1)(m {}^{2} - m + 2) \\ = 16m {}^{2} - 4m {}^{2} + 4m - 8 > 0 \\ = 12m {}^{2} + 4m - 8 = 0 \: \\ 3m {}^{2} + m - 2 = 0 \\ = (3m - 2)(m + 1) = 0 \\ ans : m = \frac{2}{3} \: \: i = m = 1$