Discriminant and Multiplicity

​Finding the discriminant

Multiple Choice

1 What does the discriminant tell us?

• The maximum or minimum

• The y-intercept

• The number and type of solutions

• The axis of symmetry

Multiple Choice

The discriminant is

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

• ​A positive discriminant indicates that the quadratic has two distinct real number solutions.
  

• A discriminant of zero indicates that the quadratic has a repeated real number solution.

• A negative discriminant indicates that neither of the solutions are real numbers. They are complex numbers.

Drag and Drop

A ​ ​

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discriminant indicates that the quadratic has two distinct real number solutions.

A discriminant of​

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indicates that there is one real solution that is repeated.

A​

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discriminant indicates that there are no real solutions. These solutions are​

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numbers

Drag these tiles and drop them in the correct blank above

positive

zero

negative

complex

integer

whole number

rational number

Multiple Choice

If the discriminant is positive, then the solution will be

• one real solution

• two real solutions

• no real solutions

• one imaginary solution

Match

Match the following

• $$6x^2+10x+1=0$$

• $$x^2-9x-2=0$$

• $$9x^2+x+7=0$$

• $$x^2-8x+16=0$$

D=76

2 real solutions

D=89

2 real solutions

D=-251

2 complex solutions

D=0

1 real solution

• D=76

  2 real solutions

• D=89

  2 real solutions

• D=-251

  2 complex solutions

• D=0

  1 real solution

Multiple Choice

For the function below, is the discriminant positive, negative, or zero?

___________

y = x² + 4x + 4

• Positive

• Negative

• Zero

• Not Sure

Multiple Choice

What is the discriminant of -2x² − x − 1 = 0

• 76

• -7

• 9

• none of these

Multiplicity

Multiple Choice

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

• 0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)
• 2 (Mult of 3), 7 (mult 1)
• 0, 2, 7
• 2 (mult of 2), 7 (mult of 3)

Multiple Choice

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4 with Degree: 7

• (x + 5)³(x - 9)²(x + 2)(x - 4)
• (x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷
• (x + 5)³(x - 9)²(x + 2)
• (x + 5)(x - 9)(x + 2)(x - 4)

Multiple Choice

A polynomial function has zeros at -1,2, and 7 (all multiplicity of 1). Write a function rule that could represent this function.

• $$f\left(x\right)=\left(x+1\right)\left(x-2\right)\left(x-7\right)$$

• $$f\left(x\right)=\left(x-1\right)\left(x+2\right)\left(x+7\right)$$

• $$f\left(x\right)=\left(x+1\right)^2\left(x-2\right)^2\left(x-7\right)^2$$

• $$f\left(x\right)=\left(x-1\right)^2\left(x+2\right)^2\left(x+7\right)^2$$

Multiple Choice

Determine the zeros and multiplicity for the function:

$$f\left(x\right)=\left(x-2\right)^3\left(x+1\right)^2\left(x-9\right)^5$$  

• $$2m3,\ -1m2,\ 9m5$$  

• $$-2m3,\ 1m2,-9m5$$  

• $$3m2,\ 2m-1,\ 5m9$$  

• $$2m3,\ 1m2,\ 9m5$$  

Multiple Choice

Determine the values of

a, b, and c for

the quadratic equation:

4x² – 8x = 3

• a = 4, b = -8, c = 3

• a = 4, b =-8, c =-3

• a = 4, b = 8, c = 3

• a = 4, b = 8, c = -3

Multiple Choice

When in standard form, what is the value of a, b and c in this quadratic?

7x² - 4x + 3 = 5x² + 8

• a = 2 b = -4 c = -5

• a = 7 b = -4 c = 3

• a = 2 b = -4 c = 5

• a = 12 b = -4 c = -5

Multiple Choice

What is this formula?

• This is the speed of light formula.
• This is the quadratic formula.
• This is the zero product property.
• This is scary.

Multiple Choice

The quadratic formula can be used to solve quadratic equations that can or cannot be factored.

• True

• False

Multiple Choice

Use the quadratic formula to solve 2x² + 2x - 12?

• -2, 3
• 2, 3
• 2, -3
• -2, -3