Question

Write a quadratic polynomial whose zeros are root three pluse one,root three minus one

Answer 1

$\underline{\underline{\pink{\textbf{Step - By - Step - Explanation : -}}}}$

To Find :

• We need to find the quadratic polynomial.

Solution :

• zeroes of quadratic polynomial are √3 + 1 or √3 - 1

Let α = √3 + 1 and β = √3 - 1

Sum of zeroes :-

α + β = (√3 + 1) + (√3 - 1)

α + β = 2√3

Product of zeroes :-

αβ = (√3 + 1)(√3 - 1)

αβ = √3² - 1²

αβ = 3 - 1

αβ = 2

Required polynomial is :-

= x² - (α + β)x + αβ

= x² - (2√3)x + 2

= x² - 2√3x + 2

$\large\dag \large { \red{\underline{\bf{Hence }}}}$

$\boxed{\underline{\blue{\bf{Required\: polynomial \:is \:x^{2} - 2\sqrt{3}x + 2}}}}$

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