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If alpha and beta are roots of the equation x^2+root alpha (x)+ beta=0,then find alpha square+ beta square |
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Answer» Step-by-step explanation:In a quadratic equation of FORM ax² + bx + c = 0, Sum of ROOTS = -b/a, PRODUCT of roots = c/a.Now in equation, x² + √αx + β = 0, a = 1, b = √α, c = βSum of roots, α + β = -b/a = -√α/1 = -√α.Product of roots, αβ = c/a = β/1 = β.We know that a² + b² = (a + b)² - 2ab=> α² + β² = (α + β)² - 2αβ = (-√α)² - 2(β) = α - 2β. |
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