Question

Find the quadratic polynomial the sum of whose sum are √2 and their product is 1/3

Answer 1

quadratic eqn if roots are given

x^2 - (sum of roots )x + product of roots

x^2 - √2x + 1/3

3x^2 - 3√2x + 1 = 0

hope it helped you

Answer 2

$\alpha + \beta = \sqrt{2 } \\ \alpha \beta = \frac{1}{3 } \\ by \: formula \\ {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ = {x}^{2} - \sqrt{2}x + \frac{1}{3} = 0 \\ = \frac{3 {x}^{2} - 3 \sqrt{2}x + 1 }{3} = 0 \\ = 3 {x}^{2} - 3 \sqrt{2} + 1$