If α and β are the zeroes of the polynomial 6y 2 − 7y + 2, find a quadratic polynomial whose zeroes are 1 α and 1 β .

Question

asked Dec 18, 2022 138k views

1 Answer

Tvgemert · Answer 1 · 2022-12-22T09:13:20+0000

Answer:

Explanation:

We are given that
$\alpha$ and
$\beta$ are the zeroes of the polynomial
6y^2-7y+2

y^2-(7)/(6)y+(1)/(3)

We have to find a quadratic polynomial whose zeroes are
$1/\alpha$ and
$1/\beta$ .

General quadratic equation

$x^2-(sum\;of\;zeroes)x+ product\;of\;zeroes$

We get

$\alpha+\beta=(7)/(6)$

$\alpha \beta=(1)/(3)$

$(1)/(\alpha)+(1)/(\beta)=(\alpha+\beta)/(\alpha \beta)$

$(1)/(\alpha)+(1)/(\beta)=(7/6)/(1/3)$

$(1)/(\alpha)+(1)/(\beta)=(7)/(6)* 3=7/2$

$(1)/(\alpha)* (1)/(\beta)=(1)/(\alpha \beta)$

$(1)/(\alpha)* (1)/(\beta)=(1)/(1/3)=3$

Substitute the values

y^2-(7/2)y+3=0

Hence, the quadratic polynomial whose zeroes are
$1/\alpha$ and
$1/\beta$ is given by