Question

Find a quadratic plynomial whose sum and product of zeroes are -3/2under root 5 and 1/2 respectively.

Answer 1

2x² +3√5x -1=0.......

Answer 2

$\alpha + \beta = \frac{ - 3}{2 \sqrt{5} } \\ \alpha \beta = \frac{1}{2} \\ Polynomial = {x}^{2} - ( \alpha + \beta )x + ( \alpha \beta ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} - \bigg( \frac{ - 3}{2 \sqrt{5} } \bigg)x + \frac{1}{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2x \sqrt{5} + 3 + \sqrt{5}$