If alpha and beta are the …
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Sia ? 6 years, 7 months ago
{tex}\alpha \ and\ \beta{/tex} are the roots of the polynomial, p(y) = 25p2 - 15p + 2
a = 25, b= -15, c= 2
{tex} \alpha + \beta =-\frac{b}{a}= - \left( - \frac { 15 } {25 } \right) = \frac 35{/tex}
and {tex}\alpha \beta = \frac{c}{a} = \frac { 2 } { 25 }{/tex}
Now, {tex}\frac { 1 } { \alpha } + \frac { 1 } { \beta } = \frac { \alpha + \beta } { \alpha \beta } = \frac { 3 / 5 } { 2 /25 } = \frac { 15 } { 2 }{/tex}
and {tex}\frac { 1 } { \alpha } \times \frac { 1 } { \beta } = \frac { 1 } { \alpha \beta } = \frac { 1 } { 2 / 25 } = \frac{25}{2}{/tex}.
The equation of polynomial which has {tex}\frac{1}{\alpha} \ and \ \frac{1}{\beta}{/tex}as roots is {tex}y ^ { 2 } - \frac { 15 } {2 } y + \frac{25}{2} {/tex}
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