SOLUTION: Can you please help with this equation? Find the roots of 3x^2+2x-4=0. Thank you so much for your help.

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Question 86176: Can you please help with this equation?
Find the roots of 3x^2+2x-4=0.
Thank you so much for your help.
Answer by jim_thompson5910(28595) About Me  (Show Source):
You can put this solution on YOUR website!
Starting with the general quadratic

ax%5E2%2Bbx%2Bc

the general form of 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%2B2%2Ax-4

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



x+=+%28-2+%2B-+sqrt%28+4-4%2A3%2A-4+%29%29%2F%282%2A3%29 Square 2 to get 4



x+=+%28-2+%2B-+sqrt%28+4%2B48+%29%29%2F%282%2A3%29 Multiply -4%2A-4%2A3 to get 48



x+=+%28-2+%2B-+sqrt%28+52+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-2+%2B-+2%2Asqrt%2813%29%29%2F%282%2A3%29 Simplify the square root



x+=+%28-2+%2B-+2%2Asqrt%2813%29%29%2F6 Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

x+=+%28-2+%2B+2%2Asqrt%2813%29%29%2F6 or x+=+%28-2+-+2%2Asqrt%2813%29%29%2F6


Which approximate to

x=0.86851709182133 or x=-1.535183758488


So our solutions are:
x=0.86851709182133 or x=-1.535183758488

Notice when we graph 3%2Ax%5E2%2B2%2Ax-4 we get:



when we use the root finder feature on our calculator, we find that x=0.86851709182133 and x=-1.535183758488.So this verifies our answer