Question

If α(alpha) and β(beta) are the zeroes of the quadratic polynomial f(t)= t^2 - 5t + 3, then the value of α^4β^3 + α^3β^4 is?

Answer 1

Answer:

is 135

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given: α and β are the zeroes of quadratic polynomial f(t) = t² - 5t + 3

$\mathsf{\implies Sum\;of\;the\;Roots\;(\alpha + \beta) = \dfrac{5}{1} = 5}$

$\mathsf{\implies Product\;of\;the\;Roots\;(\alpha.\beta) = \dfrac{3}{1} = 3}$

$:\implies$  α⁴β³ + α³β⁴

$:\implies$  α³β³(α + β)

$:\implies$  (αβ)³(α + β)

$:\implies$  (3)³(5)

$:\implies$  (27 × 5)

$:\implies$  135