Question

If α and β are the zeroes of the quadratic polynomial f(x)=ax 2 + b x+ c, then evaluate ​​a(α 2 /β+β 2 /α) + b(α/β+β/α)

Answer 1

α,β are the zeros of the quadratic polynomial f(x)=ax²+bx+c
then , α+β=-b/a and α×β=c/a
a(α²/β+β²/α)+b(α/β+β/α)
=a(α³+β³)/αβ+b(α²+β²)/αβ
=a{(α+β)³-3αβ(α+β)}/αβ+b.{(α+β)²-2αβ}/αβ
=a{(-b/a)³-3c/a(-b/a)}/(c/a)+b{(-b/a)²-2c/a}(c/a)
=a²{(-b³/a³)+3bc/a²}/c+ab{(b²/a²)-2c/a}/c
=(-b³/a+3bc)/c+(b³/a-2bc)/c
=(-b³a+3bc+b³a-2bc)/c
=bc/c
=b

Answer 2

Answer:

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Step-by-step explanation:

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