Question

If sum of zeroes of x2 +(5m-7)x - (2m-7) is four times of its product of zeroes. Find m.

Answer 1

let alpha and beta are zeros of polynomial
$\alpha + \beta = \frac{ - 5m + 7}{1} \\ \alpha \beta = - 2m + 7 \\ \alpha + \beta = 4 \alpha \beta \\ - 5m + 7 = 4( - 2m + 7) \\ - 5m + 7 = - 8m + 28 \\ - 5m + 8m = 28 - 7 \\ 3m = 21 \\ m = \frac{21}{3} \\ m = 7 \: \: \: \: \: ans$