Question

If Alpha and beta are the zeros of the polynomial 2x square + 7x + 5 find the value of 1 by Alpha square + 1 by beta square​

Answer 1

$\Huge{\textbf{\textsf{{\purple{Ans}}{\pink{wer}}{\color{pink}{:}}}}}$

$\alpha \: \: and \: \beta \: \: are \: the \: zeros \: of \: the \\ \: polinolial \: \: \: 2 {x}^{2} + 7x + 5 \\ so \\ \\ \alpha + \beta = - \frac{7}{2} \\ \\ \alpha \beta = \frac{5}{2}$

Now,

$\frac{1}{ { \alpha }^{2} } + \frac{1}{ { \beta }^{2} } \\ = \frac{ { \alpha }^{2} + { \beta }^{2} }{ { \alpha }^{2} { \beta }^{2} } \\ = \frac{ {( \alpha + \beta )}^{2} - 2 \alpha \beta }{ {( \alpha \beta )}^{2} } \\ = \frac{ {( - \frac{7}{2} )}^{2} - 2 \times \frac{5}{2} }{ {( \frac{5}{2}) }^{2} } \\ = \frac{ \frac{29}{4} }{ \frac{25}{4} } \\ = \frac{29}{25}$

Answer 2

29/25 is your answer!

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