Question

find a quadratic polynomial whose zeros are -5/4,1/2​

Answer 1

Given, the zeros

$\alpha = \frac{ - 5}{4} \\ \beta = \frac{1}{2} \\ \\ sum \: of \: zeroes \\ \alpha + \beta \\ = \frac{ - 5}{4} + \frac{1}{2} \\ = \frac{ - 5 + 2}{4} \\ = \frac{ - 3}{4} \\ \\ and \: product \: \\ \\ \alpha \beta \\ = \frac{ - 5}{4} \times \frac{1}{2} \\ = \frac{ - 5}{8} \\ \\ required \: equation \\ {x}^{2} - ( \alpha + \beta ) x+ \alpha \beta = 0 \\ \\ = > {x}^{2} - \frac{ - 3}{4}x + \frac{ - 5}{8} = 0 \\ \\ = > \frac{8 {x}^{2} + 6x - 5}{8} = 0 \\ \\ = > 8 {x}^{2} + 6x - 5 = 0$