SOLUTION: Can someone please help? Solve 3x^2-5x-7=0 Find x intercepts of f(x)=3x^2-5x-7 Thanks.

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Question 132297: Can someone please help?
Solve 3x^2-5x-7=0
Find x intercepts of f(x)=3x^2-5x-7
Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2-5%2Ax-7=0 ( notice a=3, b=-5, and c=-7)




x+=+%28--5+%2B-+sqrt%28+%28-5%29%5E2-4%2A3%2A-7+%29%29%2F%282%2A3%29 Plug in a=3, b=-5, and c=-7



x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A3%2A-7+%29%29%2F%282%2A3%29 Negate -5 to get 5



x+=+%285+%2B-+sqrt%28+25-4%2A3%2A-7+%29%29%2F%282%2A3%29 Square -5 to get 25 (note: remember when you square -5, you must square the negative as well. This is because %28-5%29%5E2=-5%2A-5=25.)



x+=+%285+%2B-+sqrt%28+25%2B84+%29%29%2F%282%2A3%29 Multiply -4%2A-7%2A3 to get 84



x+=+%285+%2B-+sqrt%28+109+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)





x+=+%285+%2B-+sqrt%28109%29%29%2F6 Multiply 2 and 3 to get 6

Now break up the expression


x+=+%285+%2B+sqrt%28109%29%29%2F6 or x+=+%285+-+sqrt%28109%29%29%2F6


So these expressions approximate to

x=2.57338441815176 or x=-0.906717751485092


So our solutions are:
x=2.5734 or x=-0.9067


So that means that the x-intercepts are

(-0.9067,0) and (2.5734,0)





Notice when we graph 3%2Ax%5E2-5%2Ax-7, we get:



when we use the root finder feature on a calculator, we find that x=2.5734 and x=-0.9067.So this verifies our answer