Question

Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -3/2. Also find the zeroes

Answer 1

the quadratic polynomial is

$a( {x}^{2} - \sqrt{2} x - \frac{3}{2} )$

$\alpha + \beta = \sqrt{2 } \\ \alpha \beta = - \frac{3}{2}$

$\alpha = \frac{ \sqrt{2} + \sqrt{14} }{2}$

get

$\beta$