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

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


   

Question 85503This question is from textbook College Algebra 4th/e
: When using the quadratic formula to solve a quadratic equation
ax(squared)+bx+c=0, the discriminant is b squared-4ac. This discriminant can be positive, zero, or negative.
Please explain what the value of the discriminant means to the graph of y=ax squared bx+c.Choose the values of a,b and c to create a discriminant and graph the corresponding equation.
I do greatly appreciate your website and assistance. This question is from textbook College Algebra 4th/e

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