The equation has roots and , and the equation has roots and . find the value of and of .
We need to know two things about a quadratic equation of the
form
1. the sum of the two roots with the sign changed.
2. the product of the two roots.
We use 1 and 2 on the first equation:
Since has roots and ,
Using 1,
multiplying both sides by
Using 2,
Now we use 1 and 2 on the second equations:
Since has roots and .
Using 1,
multiplying both sides by
getting the LCD of
Combine numerators over the LCD:
Factor out on top:
Now,
since we have above that ,
and since , we can replace
by ,
and
since we have above that ,
we can replace by -2,
Multiply both sides by
Divide both sides by
So the value of is
-----------------
Using 2 on the second equation,
But since ,
Now since from above, we have ,
becomes
So the value of is
Edwin