Question

if α&βare the zeros of the quadratic polynomial 2x^2 -4x+5 find the α^2+β^2

Answer 1

α and β are the roots of the quadratic polynomial 2x² - 4x + 5 .

so, sum of roots = α + β = -(coefficient of x)/coefficient of x²
α + β = -(-4)/2 = 2 ------(1)

product of roots = αβ = constant /coefficient of x²
αβ = 5/2 -------(2)

now, α² + β² = (α + β )² - 2αβ
= 2² - 2 × 5/2
= 4 - 5
= -1

hence, α² + β² = -1