Question

Find a quadratic polynomial whose zeroes are (5-3√2) and (5+3√2)

Answer 1

Hi there !!

Let the zeros are alpha and beta.

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

3√2 will cancel.

We know that, quadratic equation will form..

S= k(x²-S(x)+P)

S= Sum of the zeros

P = Product of the zeros

S= k(x²-10x+7), where k is non-constant.

Thankyou :)