Question

Frame a quadratic polynomial whose zeroes are 5+3√2 and 5−3√2.​

Answer 1

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

x^2-10x+7

Answer 2

$\text {The quadratic equation }\: x^2 - (\alpha+\beta)\;x + \alpha\beta = 0 \: \text{has roots } \: x = \alpha \: \text{and} \: x = \beta$

$\text{For the given problem } \alpha = 5 + 3\sqrt{2} \: \text{and}\: \beta = 5 - 3\sqrt{2} \:$

$\text{Hence, } \alpha + \beta = 10 \: \text{and}\: \alpha\beta = 5^2-(3\sqrt{2})^2 = 25 - 18 = 7$

$\text{So our required quadratic polynomial is: } x^2 - 10\;x + 7 = 0$