Question

If alpha and beta are roots of the equation x^2+root alpha (x)+ beta=0,then find alpha square+ beta square

Answer 1

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 = β

Sum 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.