Question

if alpha and beta are the zeroes of the polynomial 4x^2+3x+7=0 then the value of 1/alpha +1/beta
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Answer 1

EXPLANATION.

$\sf : \implies \: \alpha \: and \: \beta \: are \: the \: zeroes \: of \: the \: polynomial \: \implies \: 4 {x}^{2} + 3x + 7 = 0$

$\sf : \implies \: sum \: of \: zeroes \: of \: quadratic \: polynomial \\ \sf : \implies \: \alpha + \beta = \frac{ - b}{a} \\ \\ \sf : \implies \: \alpha + \beta = \frac{ - 3}{4} \: \: \: ......(1)$

$\sf : \implies \: product \: of \: zeroes \: of \: quadratic \: equation \\ \sf : \implies \: \alpha \beta = \frac{c}{a} \\ \\ \sf : \implies \: \alpha \beta = \frac{7}{4} \: \: .....(2)$

To find the value of 1/a + 1/b.

$\sf : \implies \: \dfrac{1}{ \alpha } + \dfrac{1}{ \beta } \\ \\ \sf : \implies \: \frac{ \beta + \alpha }{ \alpha \beta } \\ \\ \sf : \implies \: \frac{ \dfrac{ - 3}{4} }{ \dfrac{7}{4} } \implies \: \frac{ - 3}{4} \times \frac{4}{7} = \frac{ - 3}{7}$

Therefore,

value of 1/a + 1/b = -3/7.