Question

If alpha and beta are the zeroes of the polynomial 5x^2-7x-2 find the sum of reciprocal of zeroes

Answer 1

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!}}}$

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Here is your answer
a = 5
b = -7
c = -2

Sum of Roots = -b/a
$= - \frac{( - 7)}{5} \\ = \frac{7}{5}$
Product of Roots = c/a
$= \frac{ - 2}{5}$
Now we have to find Sum of reciprocal of zeros
$= \frac{1}{ \alpha } + \frac{1}{ \beta } \\ = \frac{ \alpha + \beta }{ \alpha \beta } \\ = \frac{ \frac{7}{5} }{ \frac{ - 2}{5} } \\ = \frac{7}{5} \times \frac{5}{ - 2} \\ = \frac{ - 7}{2} \\ = - 3.5$
$\large{\red{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\underline{\underline{\underline{Hope\:it\: helps\: you}}}}}}}}}}}}}}}$

Answer 2

Hello Friend

Here is your answer

The equation is
$5 {x}^{2} - 7x - 2 = 0$
Here, a = 5
b= -7
c = -2

Now Sum of Zeros = -b/a
$\alpha + \beta = - \frac{( - 7)}{5} \\ \alpha + \beta = \frac{7}{5}$
And

Product of Zeros = c/a
$\alpha \beta = \frac{ - 2}{5}$
Now We have to find out the sum of reciprocal of zeros.

$\frac{1}{ \alpha } + \frac{1}{ \beta } \\ \\ = \frac{ \alpha + \beta }{ \alpha \beta } \\ \\put \: the \: value \: in \: it \: we \: get \\ \\ = \frac{ \frac{ - 7}{5} }{ \frac{2}{5} } \\ \\ = - \frac{7}{5} \times \frac{5}{2} \\ \\ = - \frac{7}{2}$

= - 3.5
Hope it helps you