SOLUTION: Use the quadratic formula to solve the equation. If the equation has no real number solutions, so state. x^2 + 7x + 2 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Use the quadratic formula to solve the equation. If the equation has no real number solutions, so state. x^2 + 7x + 2 = 0      Log On


   

Question 247825: Use the quadratic formula to solve the equation. If the equation has no real number solutions, so state.
x^2 + 7x + 2 = 0
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + 7x + 2 = 0
see the part below about determinant for types of solutions
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B7x%2B2+=+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%2A1%2A2=41.

Discriminant d=41 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+41+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+41+%29%29%2F2%5C1+=+-0.298437881283576
x%5B2%5D+=+%28-%287%29-sqrt%28+41+%29%29%2F2%5C1+=+-6.70156211871642

Quadratic expression 1x%5E2%2B7x%2B2 can be factored:
1x%5E2%2B7x%2B2+=+1%28x--0.298437881283576%29%2A%28x--6.70156211871642%29
Again, the answer is: -0.298437881283576, -6.70156211871642. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B2+%29