The Discriminant

The discriminant is

• aX²  + bX  +  c
• b - 4ac
• b² - 4ac
• b² + 4ac

Tags

CCSS.HSA.REI.B.4

What does the discriminant tell us?

• The maximum or minimum
• The y-intercept
• The number and type of solutions
• The axis of symmetry

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

Determine the value of the discriminant and name the nature of the solution for the following:
x² + 2x - 63
Remember:  b² - 4ac

• 256, 2 reals rational solutions
• -256, 2 non-real imaginary solutions
• 137, 2 real irrational solutions
• 123, 2 real irrational solutions

Tags

CCSS.HSA.REI.B.4

Determine the value of the discriminant and name the nature of the roots for the following:
x² + 7x + 13
Remember:  b² - 4ac

• 400, 2 real root 
• 0, 1 real root with a multiplicity of 2
• -400, 2 imaginary roots
• -3, 2 imaginary roots

Tags

CCSS.HSA-REI.B.4B

If the discriminant is zero you will have

• no real solutions
• two real solutions
• 1 real solution (multiplicity of 2)
• 1 imaginary solution

If the discriminant is positive, then the solution will be

• one real solution
• two real solutions
• no real solutions
• one imaginary solution

Tags

CCSS.HSA.REI.B.4

If the discriminant is negative, then the solution will be

• one real solution
• two real solutions
• two imaginary solutions
• one imaginary solution

Find the discriminant of the following equation.

3x² -x- 2 = 0

• 5
• 25
• -24
• -26

Tags

CCSS.HSA.REI.B.4

What are the roots of the quadratic equation:  (x-3)² = 0

• x = -3, multiplicity of 2
• x = 0, -3
• x = 0, 3
• x = 3, multiplicity of 2

What does multiplicity mean in terms of the roots of an equations?

• To clone a polynomial
• How many times a particular number is a zero for a given polynomial.
• how many times a polynomial function crosses the x-axis
• how many end behaviors a polynomial has

Tags

CCSS.HSA.APR.B.3