Question

if one root of quadratic equation is 2- √3 and sum of roots is 4 then find the quadratic equation

Answer 1

Hi friend
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Your answer
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Let the roots of the quadratic equation be α and β.

Let, α = (2 - √3)

α + β = 4

=> 2 - √3 + β = 4

=> β = 4 - 2 + √3

=> β = 2 + √3

So,

Quadratic equation = x² - (α + β)x + αβ

=> x² - 4x + (2 - √3)(2 + √3)

=> x² - 4x + {(2)² - (√3)²}

=> x² - 4x + (4 - 3)

=> x² - 4x + 1

HOPE IT HELPS