Question

If alpha and beta are the zeros of the polynomial 5 x square - 7 x + 1 then find the value of Alpha upon beta + beta upon Alpha

Answer 1

$\text{Given}$

$\mathsf{Polynomial, f(x) = 5x^2 - 7x + 1}$

$\text{To find}$

$\mathsf{Value \: of \: \frac{\alpha}{\beta} + \frac{\beta}{\alpha}}$

$\text{Solution}$

$\text{For f(x), let us find out the :}$

$\mathtt{\red{\bigstar \: Sum\: of \: zeroes = \Large{\frac{-(coefficient\: of\: x) }{coefficient\: of\: x^2}}}}$

$\mathtt{\rightarrow\: \alpha + \beta = \frac{-(-7)}{5}}$

$\mathtt{\rightarrow\: \alpha + \beta = \frac{7}{5}}$

$\mathtt{\red{\bigstar \: Product\: of \: zeroes = \Large{\frac{constant\: term }{coefficient\: of\: x^2}}}}$

$\mathtt{\rightarrow\: \alpha \beta = \frac{1}{5}}$

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$\mathtt{\implies\: \frac{\alpha}{\beta} + \frac{\beta}{\alpha} = \frac{\alpha^{2} + \beta^{2}}{\alpha\beta}}$

$\mathtt{\rightarrow\: \frac{( \alpha + \beta )^{2} - 2 \alpha \beta}{\alpha \beta}}$

$\Large{\mathtt{\rightarrow\: \frac{(\frac{1}{5})^{2} - 2(\frac{1}{5})}{\frac{1}{5}}}}$

$\Large{\mathtt{\rightarrow\: \frac{(\frac{49}{25} - \frac{2}{5})}{\frac{1}{5}}}}$

$\Large{\mathtt{\rightarrow\: \frac{49 - 10}{25} × 5}}$

$\Large{\mathtt{\rightarrow\: \frac{39}{25} × 5 }}$

$\Huge{\fbox{\mathtt{\green{\rightarrow\: \frac{39}{5}}}}}$

Answer 2

Answer:

ans is 39/5

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