Question

Find the value of 1/alpha+1/beta if alpha and beta are the zeroes of 3x^2+5x-7

Answer 1

Yo!

Here's the answer! :)

Given polynomial:3x²+5x-7

To find the value of:

$\frac{1}{ \alpha } + \frac{1}{ \beta }$

Cross multiplying them,we get–

$\frac{ \alpha + \beta }{ \alpha \beta }$

Now, we know that, sum of roots,i.e, alpha+beta= –b/a.

And product of roots,i.e, alpha × beta= c/a.

Thus,from the quadratic polynomial, 3x²+5x-7, (always in the form of ax²+bx+c)

sum of roots= –b/a= –5/3.

Product of roots= c/a= -7/3.

Now putting these into the earlier equation we found regarding alpha and beta,

we get,

-5/3 divided by -7/3

The minus sign gets cancelled,

we obtain= 5/7.

Hope it helps! :D

—TGA.