+13 Let the roots of the polynomial \(x^2 + 7x - 2 \) be \(\alpha \text{ and } \beta\) . Evaluate \(\alpha^2 + \beta^2.\)
The answer is not 4.
+16 By the quadratic formula, the roots are (-7 + √57)/2 and (-7 - √57)/2.
⍺ = (-7 + √57)/2 β = (-7 - √57)/2
⍺2 + β2 = [(-7 + √57)/2]2 + [(-7 - √57)/2]2 = 106 - 14√57 + 106 + 14√57 = 106 + 106 = 212
