6-5 The Quadratic Formula and the Discriminant A

• -160
• 80
• 40
• 128

• -160
• -144
• -176
• -200

Describe the number and type of roots if the discriminant is 128.

• Three distinct real roots

• One real root
• Two irrational roots

• Two complex roots

Describe the number and type of roots if the discriminant is -160

• No real roots
• 2 Complex roots

• One real root
• Two real roots

• x = 1/5
• x = 1/4
• x = 1/3
• x = 1/2

• x = 10 or x = -12
• x = 3 or x = -5
• x = 6 or x = -8
• x = 5 or x = -7

What should you do first if solving this equation using the FACTORING method?

x² + 6x - 13 = 3

• Get factored form

• Write down: a=1, b=6, c=-13

• Make it equal 0 by subtracting 3 on each side

• Type it all in a calculator.

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.

If the discriminant is positive, d ​ (a)   0, then there are ​ (b)   real solutions.

If the discriminant is zero, d ​ (c)   0, then there is ​ (d)   real solution.

If the discriminant is negative, d ​ (e)   0, then there are no real solutions.

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