Question

Find the quadratic polynomial find the quadratic polynomial whose sum and product of zeros are root 2 and 3 find the quadratic polynomial whose sum and product of zeros are root 2 and 3 respectively find the quadratic polynomial whose sum and product of zeros are root 2 and 3 respectively find the quadratic polynomial whose sum and product of zeros are root 2 and 3 respectively whose zeros are 3 minus root 3 by 5 and 3 + root 3 by 5

Answer 1

sum of zeros =√2
product of zeros=3
$\frac{ - b}{a} = \sqrt{2} \\ \frac{c}{a} = 3 \\ polynomial \: is \: {x}^{2} - \sqrt{2} x + 3$
2)
$\alpha = \frac{3 - \sqrt{3} }{5} \\ \beta = \frac{3 + \sqrt{3} }{5}$
$\alpha + \beta = \frac{6}{5} \\ \alpha \beta = \frac{6}{25} \\ {x}^{2} - \frac{6}{5} x + \frac{6}{25} \\ 25 {x}^{2} - 30x + 6$
is the answer

Answer 2

I hope my answer helps you