Question

Form a quadratic polynomial whose one zero is 4-√5 and the sum of zeroes is 6

Answer 1

Sum of the zeroes =alpha +beeta

Alpha +beeta=6

Let we take 4-root5 as alpha

4-root5 +beeta =6

Beeta=6-4+root5

Beeta=2+root5

Product of the zeroes =alpha*beeta

=(4-root5) *(2+root5)

=8+2root5-5

=3+2root5

$p(x) = x ^{2} - ( \alpha + \beta )x + \alpha \beta$

= x^2-6x+3+2root5