SOLUTION: I have to solve using the quadric formula and if there are no real roots , say so. Can you please help me? Page 588 Number 8 x^2 + 9x + 7 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I have to solve using the quadric formula and if there are no real roots , say so. Can you please help me? Page 588 Number 8 x^2 + 9x + 7 = 0      Log On


   

Question 146569This 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 please help me?
Page 588
Number 8
x^2 + 9x + 7 = 0 This question is from textbook Beginning Algebra

Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + 9x + 7 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B9x%2B7+=+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=%289%29%5E2-4%2A1%2A7=53.

Discriminant d=53 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-9%2B-sqrt%28+53+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%289%29%2Bsqrt%28+53+%29%29%2F2%5C1+=+-0.859945055359741
x%5B2%5D+=+%28-%289%29-sqrt%28+53+%29%29%2F2%5C1+=+-8.14005494464026

Quadratic expression 1x%5E2%2B9x%2B7 can be factored:
1x%5E2%2B9x%2B7+=+%28x--0.859945055359741%29%2A%28x--8.14005494464026%29
Again, the answer is: -0.859945055359741, -8.14005494464026. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B9%2Ax%2B7+%29

There are 2 real roots, as shown.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B9x%2B7=0 Start with the given equation.


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%289%29+%2B-+sqrt%28+%289%29%5E2-4%281%29%287%29+%29%29%2F%282%281%29%29 Plug in a=1, b=9, and c=7


x+=+%28-9+%2B-+sqrt%28+81-4%281%29%287%29+%29%29%2F%282%281%29%29 Square 9 to get 81.


x+=+%28-9+%2B-+sqrt%28+81-28+%29%29%2F%282%281%29%29 Multiply 4%281%29%287%29 to get 28


x+=+%28-9+%2B-+sqrt%28+53+%29%29%2F%282%281%29%29 Subtract 28 from 81 to get 53


x+=+%28-9+%2B-+sqrt%28+53+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-9%2Bsqrt%2853%29%29%2F%282%29 or x+=+%28-9-sqrt%2853%29%29%2F%282%29 Break up the expression.


So our answers are x+=+%28-9%2Bsqrt%2853%29%29%2F%282%29 or x+=+%28-9-sqrt%2853%29%29%2F%282%29


which approximate to x=-0.86 or x=-8.14