Question

find the polynomial whose zeroes are given as under alpha =1/2 , beta = 1/2​

Answer 1

Hey

$Given: \alpha = \beta = \frac{1}{2} \\ \\ Required \: polynomial: \\ \\ x {}^{2} - ( \alpha + \beta )x + \alpha \beta \\ \\ = x {}^{2} - ( \frac{1}{2} + \frac{1}{2} ) x+ \frac{1}{2} \times \frac{1}{2 } \\ \\ = x {}^{2} - \frac{2}{2} x + \frac{1}{4} \\ \\ = x {}^{2} - x + \frac{1}{4} \\ \\ = 4x {}^{2} - 4x + 1$