Question

Write a quadratic equation whose roots are root3+1 and root3-1

Answer 1

ANSWER:

We know that

Quadratic equation = x² - (sum of roots)x + product of roots

Given

• α = √3 + 1 , β = √3 - 1

Sum of roots (α + β) = √3 + 1 + √3 -1 = 2√3

Product of roots (αβ) = (√3 + 1)(√3 - 1)

Using

(a + b)(a - b) = a² - b²

Product of roots = (√3)² - (1)² = 3 - 1 = 2

Required quadratic equation = x² - 2√3x + 2

Hence , required quadratic equation is x² - 2√3x + 2 = 0