SOLUTION: Let's put an equation with that curve. Use y = x2-8x+7 a. What is the value of the discriminant? Review Lesson 3.05. b. What types of roots will this equation have? Ex: two com

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Let's put an equation with that curve. Use y = x2-8x+7 a. What is the value of the discriminant? Review Lesson 3.05. b. What types of roots will this equation have? Ex: two com      Log On


   

Question 147469: Let's put an equation with that curve. Use y = x2-8x+7
a. What is the value of the discriminant? Review Lesson 3.05.
b. What types of roots will this equation have? Ex: two complex roots, one repeated root, two real rational roots or two real irrational roots? Review Lesson 3.05.
c. Find the roots by factoring and solving. Review Lesson 3.04.
d. Find the roots by using the quadratic equation. Review Lesson 3.04.
e. Find the roots by graphing and using the tracking tool.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-8x%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=%28-8%29%5E2-4%2A1%2A7=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+36+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+36+%29%29%2F2%5C1+=+7
x%5B2%5D+=+%28-%28-8%29-sqrt%28+36+%29%29%2F2%5C1+=+1

Quadratic expression 1x%5E2%2B-8x%2B7 can be factored:
1x%5E2%2B-8x%2B7+=+1%28x-7%29%2A%28x-1%29
Again, the answer is: 7, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B7+%29