Question

find the quadratic polynomial whose zeroes are √2+3 and √2-3.

Answer 1

Pls refer the pic---

Answer 2

The quadratic polynomial will be $x^{2}$-2$\sqrt{2}$x

Given:

Zeroes of a quadratic polynomial= $\sqrt{2}$+3 and $\sqrt{2}$-3

Zeroes of a polynomial describe its roots.

Let $\sqrt{2}$+ 3=α and $\sqrt{2$−3=β

​Sum of the roots will be α+β = ($\sqrt{2}$+3) + ($\sqrt{2}$ -3) = 2$\sqrt{2}$

Product of the roots is represented by αβ=($\sqrt{2}$+3)($\sqrt{2}$-3)= 2-9= -7

A polynomial can be represented as $x^{2}$− (sum of the roots) x+ product of the roots=$x^{2}$ −2$\sqrt{2}$x+ (-7)=  $x^{2}$-2$\sqrt{2}$x-7

Thus, the quadratic polynomial will be $x^{2}$-2$\sqrt{2}$x-7

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