Question

If one zero of a quadratic polynomial is 2+underroot 5 and sum of zeroes is 4. find the quadratic polynomial

Answer 1

If one root is irrational other will be its conjugate ( always)

Other root will be 2 - root(5)

Sum of roots = 4
Product of roots = (2+root(5))x (2-root(5)) = - 1

Equation = x2 +(sum of roots) x + product of roots =0

= x2 - 4x-1 =0

Answer 2

Let the second zero be 'b'
thus, 2+√5 + b = 4
b = 2-√5
Product of zeroes = (2+√5)(2-√5)
= 4-5 = -1
For eq.
x^2 - (sum of zeroes)x + (product of zeroes) = 0
x^2 - (4)x + (-1) = 0
x^2 -4x -1 = 0

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