Question

find the quadratic polynomial whose zeros are root2+root3 and root2-root3​

Answer 1

$\alpha = \sqrt{2} + \sqrt{3}$

$\beta = \sqrt{2} - \sqrt{3}$


Standard form of quadratic polynomial-

P(x) = k{x^2 -(alpha+beta)x + alpha×beta}

Where k is the constant


$p(x) = k ( {x}^{2} - ( \sqrt{2} + \sqrt{3} + \sqrt{2} - \\ \sqrt{3} )x + ( \sqrt{2} + \sqrt{3} )( \sqrt{2} - \sqrt{3} )$


p(x) = k(x^2 -2√2x + (√2)^2 -(√3)^2

p(x) = k(x^2 -2√2x +2-3)

p(x) =k(x^2 -2√2x-1)

Let k=1

p(x) = x^2 -2√2x -1

This is the required equation.


$\huge \bf{hope \: it \: helps}$