Discriminant
What is it and how do you find it?
What is it?
It is the number of solutions a quadratic has. The solutions (aka roots or zeros) are where the quadratic intersects the x-axis.
The discriminant is a number calculated by using the formula b^2-4ac.
If its value is positive (greater than zero), the quadratic has 2 solutions.
If its value is zero, the quadratic has 1 solution.
If its value is negative (less than zero), the quadratic has 2 complex (imaginary) solutions.
The discriminant is a number calculated by using the formula b^2-4ac.
If its value is positive (greater than zero), the quadratic has 2 solutions.
If its value is zero, the quadratic has 1 solution.
If its value is negative (less than zero), the quadratic has 2 complex (imaginary) solutions.
How do you find it?
Put the quadratic equation in standard for (ax^2+bx+c=0). List your a, b and c. Finally, plug the values into b^2-4ac
Try these...
Find the discriminant and describe the number and type of roots.
1. x^2-9=3x
2. 4x^2+10x+9=0
3. 9x^2+12x+4=0
1. x^2-9=3x
2. 4x^2+10x+9=0
3. 9x^2+12x+4=0
Your answers...
#1
First, put the equation in standard form. Then plug in you a, b and c. Your discriminant is 45 which means you have 2 real solutions.
#2
Plug your a, b and c into the formula. Your discriminant is -44 which means you have 2 complex (aka imaginary) solutions.
#3
Plug in a, b, and c. Your discriminant is zero which means you have 1 real solution.
What does this mean?
If you graphed #1, it would intersect the x-axis 2 times.
If you graphed #2, it would not intersect the x-axis at all.
If you graphed #3, it would sit on the x-axis, intersecting it one time.
If you graphed #2, it would not intersect the x-axis at all.
If you graphed #3, it would sit on the x-axis, intersecting it one time.