SOLUTION: When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. Create thr

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. Create thr      Log On


   

Question 71936: When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.
Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If the discriminant is greater than zero, then you will have a positive square root. This means you will have 2 roots that are real numbers.
Ex: x^2+5x+6 if you put this into the quadratic equation you get
%28-5%2B-sqrt%2825-24%29%29%2F2=%28-5%2B-sqrt%281%29%29%2F2 This further shows that the roots are real numbers of x=-2 and x=-3
graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2%2B5x%2B6+%292 real roots
If the discriminant is equal to zero, then you will have only 1 root with multiplicity of 2.
Ex: x^2+4x+4 place into quadratic formula
%28-4%2B-sqrt%2816-16%29%29%2F2=%28-5%2B-sqrt%280%29%29%2F2
graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2%2B4x%2B4+%29 1 real root with multiplicity of 2
If you have a negative discriminant, then no real roots will result since it's not possible to take the square root of a negative number and get a real result.
Ex: x^2+x+3 if placed into the quadratic formula
%28-5%2B-sqrt%281-12%29%29%2F2=%28-5%2B-sqrt%28-11%29%29%2F2
graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2%2Bx%2B3+%29No real roots, only complex roots
So a you will have a graph that doesn't cross the x-axis but will have complex roots