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in Polynomials by (38.0k points)
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If α and β are the zeros of the quadratic polynomial f(t) = t2 - 4t + 3, find the value of α4β3α3β4

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Let α and β are the roots of the given eqn

Sum of the roots

= α + β = \(\frac{Coefficient\,of\,x}{Coefficient\,of\,x^2}\) = - \(\frac{(-4)}{1}\) = 4

Product of the roots

= α x β= \(\frac{Constant\,term}{coefficient\,of\,x^2}\)\(\frac{(3)}{1}\) = 3

Now, to evaluate

α 4β 3 + α3β 4 = α3β 3(α + β)

On substituting values from above, we get

⇒ 33× 4 = 108

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