Find Solutions Using the Discriminant Slides

The discriminant is

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

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
• √(-256 - 2 imaginary solutions
• √(137) - 2 reals - Irrational
• 123 - 2 reals - Rational

Determine the value of the discriminant and name the nature of the solution for the following:
x² + 8x - 84
Remember:  b² - 4ac

• 256 - 2 reals - Rational
• 400 - 2 reals - Rational
• √(-400) - 2 non-real complex - imaginary
• 20 - 2 reals - Rational

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

• 400 - 2 reals
• 0 - 1 real
• √(-400) - 2 non-real complex - imaginary
• -3 ---- 2 non-real complex - imaginary

What does the discriminant tell us?

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

If the discriminant is negative, how many solutions and of what type?

• 1 real solution
• 2 irrational solutions
• 2 complex solutions

If the discriminant is positive, how many solutions and of what type?

• 1 real solution
• 2 real solutions
• 2 complex solutions

If the discriminant is 13, how many solutions and of what type? 

• 1 real solution
• 2 irrational solutions
• 2 rational solutions
• 2 complex solutions

Find the discriminant of the quadratic equation:
2x² + 10x - 15 = 0

• 25
• -20
• 220
• 92

Solve Using the Quadratic Formula 
2x² + 7x - 15 = 0

• -1.5 or 5
• No Solution
• -5 or 1.5
• 0.7 or 5