SOLUTION: I have to solve using the quadric formula and if there are no real roots say so. Can you help me please? Page 588 Number 10 3x^2 + 7x - 6 = 0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I have to solve using the quadric formula and if there are no real roots say so. Can you help me please? Page 588 Number 10 3x^2 + 7x - 6 = 0      Log On


   

Question 146570This question is from textbook Beginning Algebra
: I have to solve using the quadric formula and if there are no real roots say so. Can you help me please?
Page 588
Number 10
3x^2 + 7x - 6 = 0 This question is from textbook Beginning Algebra

Found 2 solutions by Alan3354, Earlsdon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2+%2B+7x+-+6+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B7x%2B-6+=+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=%287%29%5E2-4%2A3%2A-6=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+121+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+121+%29%29%2F2%5C3+=+0.666666666666667
x%5B2%5D+=+%28-%287%29-sqrt%28+121+%29%29%2F2%5C3+=+-3

Quadratic expression 3x%5E2%2B7x%2B-6 can be factored:
3x%5E2%2B7x%2B-6+=+%28x-0.666666666666667%29%2A%28x--3%29
Again, the answer is: 0.666666666666667, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B7%2Ax%2B-6+%29

2 real roots, -3 and +2/3.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve using the quadratic formula: x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
3x%5E2%2B7x-6+=+0 In this problem, a = 3, b = 7, and c = -6
Make the appropriate substitutions into the formula:
x+=+%28-7%2B-sqrt%287%5E2-4%283%29%28-6%29%29%29%2F2%283%29 Simplify.
x+=+%28-7%2B-sqrt%2849-%28-72%29%29%29%2F6
x+=+%28-7%2B-sqrt%28121%29%29%2F6
x+=+%28-7%2B11%29%2F6 or x+=+%28-7-11%29%2F6
x+=+2%2F3 or x+=+-3 There are two real roots.