Question

Find a quadratic polynomial whose zeroes are: –2+1/√2, 2−1/√2

Answer 1

Given: –

α + β = 2+1/√2 + 2−1/√2 = 4.

αβ = (2+1/√2)(2-1/√2)=4−1/2=7/2

∴ If α and β are zeroes of any quadratic polynomial, then the quadratic polynomial equation can be written directly as: –

x2 – (α+β)x +αβ = 0

Thus, the required quadratic polynomial equation will be :-

x2 – (4)x −7/2 = 0

2x2−8x+7 = 0.