SOLUTION: I am having trouble trying to solve this problem. Would someobdy be able to assist me? Solve - 3x^2 - 7x - 5 = 0 a. The solutions(s) is/are x=? b. Find the x-intercepts of

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Question 515573: I am having trouble trying to solve this problem. Would someobdy be able to assist me?
Solve - 3x^2 - 7x - 5 = 0
a. The solutions(s) is/are x=?
b. Find the x-intercepts of f(x) = 3x^2 -7x - 5.
1/3 x 3x^2 - 7/3x - 5/3 = 0
x^2 - 7/3x - 5/3 = 0
x^2 - 7/3x - 5/3 this is where I get lost.
Thank you.
Sincerely,
Christine Fitzgerald
Found 2 solutions by drcole, Alan3354:
Answer by drcole(72)   (Show Source): You can put this solution on YOUR website!
You are given the quadratic equation

It looks like you are trying to factor this quadratic, but the easiest way to solve this one is to use the quadratic formula: recall that the solutions to

are

Here, a = -3, b = -7, and c = -5, so we substitute in and get:

(simplifying)
(simplifying)
(since )
So the two solutions are:

and

Now, the x-intercepts of the graph of are the REAL roots of . If the quadratic equation has no real roots, then the graph never intersects the x-axis: it is either always above the x-axis, or always below it. In this case, the solution to the quadratic equation are non-real complex numbers, so there are no x-intercepts of f(x).
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Find the x-intercepts of f(x) = 3x^2 -7x - 5.
1/3 x 3x^2 - 7/3x - 5/3 = 0
x^2 - 7/3x - 5/3 = 0
x^2 - 7/3x - 5/3 this is where I get lost.
Add 5/3 to both sides
x^2 - 7/3x = 5/3
To complete the square, you have to add c, which is (b/2a)^2

c = 49/36
Add that to both sides

Now,



----------------------------
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=109 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2.90671775148509, -0.573384418151758. Here's your graph:

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The other tutor used -3 for the x^2 term.
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