Question

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Answer 1

formula used (a+b)^2 = a^2 + b^2+ 2ab

Answer 2

Step-by-step explanation:

Given Equation is f(x) = x² - px + q.

Here, a = 1, b = -p, c = q.

α and β are the zeroes of the quadratic polynomial.

(i) Sum of roots:

α + β = -b/a

α + β = p

(ii) Product of roots:

αβ = c/a

αβ = q

LHS:

= (α²/β²) + (β²/α²)

= (α² + β²)/(αβ)²

= [(α² + β²)² - 2(αβ)²]/(αβ)²

= [[(α + β)² - 2αβ]² - 2(αβ)²]/(αβ)²

= [[(p)² - 2q]² - 2q²]/q²

= [p⁴ + 4q² - 2p².2q - 2q²]/q²

= [p⁴ + 2q² - 4p²q]/(q)²

= (p⁴/q²) + 2 - (4p²/q)

= (p⁴/q²) - (4p²/q) + 2

RHS

Hope it helps!