Question

please solve it as soon as possible
3rd question

Answer 1

Hey There!!

Here, we are given the following data:

$f(t)=t^2-4t+3 \\ \\ \\ \alpha \,\, and \,\,\beta \textrm{ are zeroes} \\ \\ \\ \implies \alpha + \beta = -\frac{\textrm{Coefficient of t}}{\textrm{Coefficient of }t^2} = -\frac{(-4)}{1} = 4 \\ \\ \\ \boxed{\alpha + \beta=4} \\ \\ \\ \\ And \, \, \alpha \beta = \frac{\textrm{Constant Term}}{\textrm{Coefficient of }t^2} = \frac{3}{1} = 3 \\ \\ \\ \implies \boxed{\alpha \beta = 3}$



Now, we can find the required value easily:

$\alpha^4 \beta^3 + \alpha^3 \beta^4 \\ \\ \\ =\alpha^3 \beta^3 (\alpha + \beta) \\ \\ \\ = 3^3 \times (4) = 27 \times 4 = 108 \\ \\ \\ \\ \implies \boxed{\alpha^4 \beta^3 + \alpha^3 \beta^4 = 108}$



Thus, your answer is 108.


Hope it helps
Purva
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