Question: 10
If α and β are the zeroes of the quadratic polynomial
f(t) = t2 – 4t + 3, find the value of α4β3 + α3β4.
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Solution:
Since, α and β are the zeroes of the quadratic polynomial f(t) = t2 – 4t + 3
So, Sum of the zeroes = α + β = 4
Product of the zeroes = α × β = 3
Now,
α4β3 + α3β4 = α3β3(α + β)
= (3)3(4) = 108
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