write the quadratic equation whose roots are 2 + root 3 and 2 minus root 3
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Given,
Roots of equation = 2 + √3 and 2 - √3
So, sum of zeroes
α + β = 2 + √3 + 2 - √3
α + β = 4
And, product of zeroes
αβ = ( 2 + √3 ) ( 2 - √3 )
αβ = 4 - 3
αβ = 1
We know that
x² - (α + β)x + αβ = 0
x² - 4x + 1 = 0
Hence, the required equation is x² + 4x + 1 = 0
Given,
Roots of equation = 2 + √3 and 2 - √3
So, sum of zeroes
α + β = 2 + √3 + 2 - √3
α + β = 4
And, product of zeroes
αβ = ( 2 + √3 ) ( 2 - √3 )
αβ = 4 - 3
αβ = 1
We know that
x² - (α + β)x + αβ = 0
x² - 4x + 1 = 0
Hence, the required equation is x² + 4x + 1 = 0
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