SOLUTION: Hello, Please help A: solve 3x^2-5x-7=0 B: find the x-intercept of F(X)=3x^2-5x-7 what are the soulutions x= type an exact answers, using radicals as needed. Express c

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hello, Please help A: solve 3x^2-5x-7=0 B: find the x-intercept of F(X)=3x^2-5x-7 what are the soulutions x= type an exact answers, using radicals as needed. Express c      Log On


   

Question 332417: Hello, Please help
A: solve 3x^2-5x-7=0
B: find the x-intercept of
F(X)=3x^2-5x-7
what are the soulutions x=
type an exact answers, using radicals as needed. Express complex numbers in terms of i use a comma to separate
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-5x%2B-7+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-5%29%5E2-4%2A3%2A-7=109.

Discriminant d=109 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+109+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+109+%29%29%2F2%5C3+=+2.57338441815176
x%5B2%5D+=+%28-%28-5%29-sqrt%28+109+%29%29%2F2%5C3+=+-0.906717751485092

Quadratic expression 3x%5E2%2B-5x%2B-7 can be factored:
3x%5E2%2B-5x%2B-7+=+%28x-2.57338441815176%29%2A%28x--0.906717751485092%29
Again, the answer is: 2.57338441815176, -0.906717751485092. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-5%2Ax%2B-7+%29