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Question
If α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of α4β3 + α3β4.
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Solution
From the question, it is given that:
α and β are the roots of the quadratic polynomial f(t) where a = 1, b = −4 and c = 3
Sum of the roots = α + β = `(-b)/a`
= `-((-4))/1`
= 4
Product of the roots = αβ = `c/a`
= `3/1`
= 3
α4β3 + α3β4
⇒ α3β3 (α +β)
⇒ (αβ)3 (α +β)
⇒ (3)3 (4)
⇒ 27 × 4
⇒ 108
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