Question

If the roots of the quadratic equation x2 – m(2x – 5) – 6 =0 are equal,

then m =

​

Answer 1

Answer:

$m = 2 \: \: \: or \: \: \: \: 3.$

Step-by-step explanation:

${x}^{2} - m(2x - 5) - 6 = 0 \\ \\ {x}^{2} - 2mx + (5m - 6) = 0 \\ \\ {b }^{2} - 4ac = 0 \\ \\ {( - 2m)}^{2} - 4(5m - 6) = 0 \\ \\ 4 {m}^{2} - 20m + 24 = 0 \\ \: \: \\ \\ {m}^{2} - 5m + 6 = 0 \\ \\ {m}^{2} - 3m - 2 m + 6 = 0 \\ \\ m(m - 3) - 2(m - 3) = 0 \\ \\ (m - 2)(m -3) = 0 \\ \\ m = 2 \: \: \: or \: \: \: \: 3.$