SOLUTION: Please help. Here is one that says solve and then find the x intercept. 3x^2-5x-11=0 When I used the quadratic equation I came up with an answer of 5+square root of 157 divid

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help. Here is one that says solve and then find the x intercept. 3x^2-5x-11=0 When I used the quadratic equation I came up with an answer of 5+square root of 157 divid      Log On


   

Question 176902: Please help. Here is one that says solve and then find the x intercept.
3x^2-5x-11=0
When I used the quadratic equation I came up with an answer of
5+square root of 157 divided by 6 AND 5-square root of 157 divided by 6.
Then when I found the x intercept my answers were x=5/6 and y=-107/12.
This does not seem right to me. Is it? Thank you
Found 2 solutions by vleith, josmiceli:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
As you can see, the two values you get from solving the quadratic equation ARE the x intercepts. That what it means to be a 'root'
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-5x%2B-11+=+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-11=157.

Discriminant d=157 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+157+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+157+%29%29%2F2%5C3+=+2.92166068102361
x%5B2%5D+=+%28-%28-5%29-sqrt%28+157+%29%29%2F2%5C3+=+-1.25499401435694

Quadratic expression 3x%5E2%2B-5x%2B-11 can be factored:
3x%5E2%2B-5x%2B-11+=+3%28x-2.92166068102361%29%2A%28x--1.25499401435694%29
Again, the answer is: 2.92166068102361, -1.25499401435694. 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-11+%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2+-+5x+-+11+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+3
b+=+-5
c+=+-11
x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A3%2A%28-11%29+%29%29%2F%282%2A3%29+
x+=+%285+%2B-+sqrt%28+25+%2B+132+%29%29%2F6+
x+=+%285+%2B-+sqrt%28+157+%29%29%2F6+
x+=+%285+%2B+sqrt%28157%29%29%2F6
x+=+%285+-+sqrt%28157%29%29%2F6
I'm confused by "x-intercept"
By definition, the x-intercept is where y=0
and that would be the 2 roots I just solved for
The y-intercept, however, would be where x=0
y+=+3x%5E2+-+5x+-+11+
y+=+3%2A0%5E2+-+5%2A0+-+11
y+=+-11 or the point (0,-11)
The plot:
+graph%28+500%2C+500%2C+-10%2C+10%2C+-15%2C+15%2C+3x%5E2+-+5x+-+11%29+