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If alpha and beta are zeroes …

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If alpha and beta are zeroes of polynomial 6y^2-7y+2 find quadratic polynomial whose zeroes are 1÷alpha and1÷beta

Posted by Rajni Hada 5 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 5 years, 10 months ago

$\alpha \ and\ \beta$ are the roots of the polynomial, p(y) = 6y² - 7y + 2
a=6, b= -7, c= 2
$\alpha + \beta =-\frac{b}{a}= - \left( - \frac { 7 } { 6 } \right) = \frac { 7 } { 6 }$
and $\alpha \beta = \frac{c}{a} = \frac { 2 } { 6 } = \frac { 1 } { 3 }$
Now, $\frac { 1 } { \alpha } + \frac { 1 } { \beta } = \frac { \alpha + \beta } { \alpha \beta } = \frac { 7 / 6 } { 2 / 6 } = \frac { 7 } { 2 }$
and $\frac { 1 } { \alpha } \times \frac { 1 } { \beta } = \frac { 1 } { \alpha \beta } = \frac { 1 } { 1 / 3 } = 3$ .
The equation of polynomial which has $\frac{1}{\alpha} \ and \ \frac{1}{\beta}$ as roots is $y ^ { 2 } - \frac { 7 } { 2 } y + 3 = \frac { 1 } { 2 } \left[ 2 y ^ { 2 } - 7 y + 6 \right]$

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