Question

Find the quadratic polynomial the sum and product of whose zeroes are 4 and -1/4 ​

Answer 1

Answer:

Given

$\alpha + \beta = 4 \\ \\ \alpha \beta = \frac{ - 1}{4}$

Quadratic polynomial =

${x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \\ {x}^{2} - 4x - \frac{1}{4} = 0$

To remove denominator Multiplying by 4 on each side.

$4 {x}^{2} - 16x - 1 = 0$

Hope it helps.