Question

if alpha and beta are the roots of the quadratic polynomial f(x) = ax^2 +bx + c, then evaluate alpha^2 + beta^2

Answer 1

Answer:alpha²+beta²=(alpha+beta)²-2alphabeta [(a+b)²=a²+b²+2ab]

Alpha + beta = -b/a (sum of zeroes)

Alphabeta = c/a (product of zeroes)

Alpha²+beta²=(-b/a)²-2×c/a

= b²/a²-2c/a

=(b²-ac)/a²

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