Question 412586: Determine the sum and product of the roots of 3y^2– 2y + 12 = 0
Thanks Found 2 solutions by ewatrrr, solver91311:Answer by ewatrrr(24785) (Show Source):
Hi
Determine the sum and product of the roots of
3y^2– 2y + 12 = 0
Roots are {1/3 + isqrt(35), 1/3 -isqrt(35)/3}
Sum of roots is 2/3
Product of roots is [1/3 + isqrt(35)][1/3 - isqrt(35)] = 1/9 + 35 = 35 1/9
Note i^2 = -1
Use the quadratic formula to calculate the two complex roots of the equation. Then multiply the two roots. They are complex conjugates, so the result is the SUM of two squares (not the difference because ).
The sum of the two roots is simply two times the real part because the imaginary parts are of opposite signs.
John
My calculator said it, I believe it, that settles it
