SOLUTION: Use the quadratic formula to find both solutions to the quadratic equation 3x^2-x+4=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Use the quadratic formula to find both solutions to the quadratic equation 3x^2-x+4=0      Log On


   

Question 738692: Use the quadratic formula to find both solutions to the quadratic equation 3x^2-x+4=0
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 3%2Ax%5E2-x%2B4=0 ( notice a=3, b=-1, and c=4)





x+=+%28--1+%2B-+sqrt%28+%28-1%29%5E2-4%2A3%2A4+%29%29%2F%282%2A3%29 Plug in a=3, b=-1, and c=4




x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%2A3%2A4+%29%29%2F%282%2A3%29 Negate -1 to get 1




x+=+%281+%2B-+sqrt%28+1-4%2A3%2A4+%29%29%2F%282%2A3%29 Square -1 to get 1 (note: remember when you square -1, you must square the negative as well. This is because %28-1%29%5E2=-1%2A-1=1.)




x+=+%281+%2B-+sqrt%28+1%2B-48+%29%29%2F%282%2A3%29 Multiply -4%2A4%2A3 to get -48




x+=+%281+%2B-+sqrt%28+-47+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




x+=+%281+%2B-+i%2Asqrt%2847%29%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%281+%2B-+i%2Asqrt%2847%29%29%2F%286%29 Multiply 2 and 3 to get 6




After simplifying, the quadratic has roots of


x=1%2F6%2Bsqrt%2847%29%2F6%2Ai or x=1%2F6-sqrt%2847%29%2F6%2Ai