SOLUTION: I tried everything to solve this problem but I can't figure out how. I think the answer is an imaginary number. PLEASE HELP!!! :) If the zeros of f(x)= 4x^2 + 3x + 2 are A a

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: I tried everything to solve this problem but I can't figure out how. I think the answer is an imaginary number. PLEASE HELP!!! :) If the zeros of f(x)= 4x^2 + 3x + 2 are A a      Log On


   

Question 20736: I tried everything to solve this problem but I can't figure out how. I think the answer is an imaginary number. PLEASE HELP!!! :)
If the zeros of f(x)= 4x^2 + 3x + 2 are A and b, find the value of 1/A +1/B.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, first you need to solve the quadratic. It doesn't factor so use the quadratic formula: x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
x=%28-3%2B-sqrt%289-32%29%29%2F8
x=%28-3%2B-sqrt%28-23%29%29%2F8
The roots are:
A+=+-3%2F8+%2B+%281%2F8%29sqrt%2823%29i
B+=+-3%2F8+-+%281%2F8%29sqrt%2823%29i
To find 1%2FA+%2B+1%2FB first simplify to: %28A%2BB%29%2FAB
= -6%2F8+=+-3%2F4
AB+=+%28-3%2F8+%2B+%281%2F8%29sqrt%2823%29i%29%28-3%2F8+-+%281%2F8%29sqrt%2823%29i%29 = 9%2F64+-+%281%2F64%29%2823%29i%5E2 + 9%2F64+%2B+23%2F64+=+32%2F64 = 1%2F2
Finally, %28A%2BB%29%2FAB+=+%28-3%2F4%29%2F%281%2F2%29 = %28-3%2F4%29%282%29+=+-3%2F2