Question

If α and β are the zeros of the quadratic polynomial f(t) = t² - 4t + 3, find the value of (α⁴β³ + α³β⁴).

Answer 1

Step-by-step explanation:

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Answer 2

(α⁴β³ + α³β⁴) = 108

Step-by-step explanation:

f(t) = t² - 4t + 3

α and β are roots of the polynomial. So product of the roots = c/a = 3/1 = 3 = αβ

Sum of the roots = α + β = -b/a = -(-4)/1 = 4

(α⁴β³ + α³β⁴) = α³β³(α + β) = (αβ)³ (α + β) = 3³ * 4 = 27 * 4 = 108