Question

if alpha and beta are the zeroes of the quadratic polynomial ax square + bx + c then evaluate alpha upon beta + beta upon alpha

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Answer 1

Answer :

α/β + β/α = $\frac{{b}^{2} - 2ac}{ac}$

Solution :

ax² + bx + c = 0

Zeroes of polynomial are α and β.

→ α/β + β/α

→ (α² + β²)/αβ

→ (α² + β²) can be written as (α + β)² - 2αβ

→ [(α + β)² - 2αβ]/αβ

→ [(-b/a)² - 2(c/a)]/(c/a)

→ (b²/a² - 2c/a)/(c/a)

→ b² - 2ca/ac

Therefore,

α/β + β/α = $\frac{{b}^{2} - 2ac}{ac}$