Question

If alpha + beta is the roots of 5x2+px-1=0 then alpha -beta=1 find p

Answer 1

Hope this answer helped you .

Answer 2

$Given \: \alpha \:and \:beta \: are \: roots \\of \: 5x^{2} + px - 1 = 0$

$i) Sum \: of \:the \: zeroes = \frac{- coefficient \:of \:x }{ coefficient \:of \:x^{2}}$

$\implies \alpha + \beta = \frac{-p}{5} \: --(1)$

$ii Product \: of \:the \: zeroes = \frac{ constant }{ coefficient \:of \:x^{2}}$

$\implies \alpha \beta = \frac{-1}{5} \: --(2)$

$\alpha - \beta = 1 \: (given)$

/* On squaring both sides , we get */

$\implies (\alpha - \beta )^{2}= 1^{2}$

$\implies (\alpha + \beta )^{2} - 4 \alpha \beta= 1$

$\implies \Big( \frac{-p}{5}\Big)^{2} - 4 \times \Big( \frac{-1}{5}\Big) = 1$

$\implies \frac{p^{2}}{25} + \frac{4}{5} = 1$

$\implies \frac{p^{2}}{25} = 1- \frac{4}{5}$

$\implies \frac{p^{2}}{25} = \frac{5-4}{5}$

$\implies \frac{p^{2}}{25} = \frac{1}{5}$

$\implies p^{2} = \frac{25}{5}$

$\implies p^{2} = 5$

$\implies p = \pm \sqrt{5}$

Therefore.,

$\red { Value \: of \:p } \green {= \pm \sqrt{5} }$

•••♪