Solving Quadratic Equations by the Quadratic Formula

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Solving Quadratic Equations by the Quadratic
Formula
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THE QUADRATIC FORMULA

• When you solve using completing the square on
  the general formula you get
• This is the quadratic formula!
• Just identify a, b, and c then substitute into
  the formula.

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WHY USE THE QUADRATIC FORMULA?

• The quadratic formula allows you to solve ANY
  quadratic equation, even if you cannot factor it.
• An important piece of the quadratic formula is
  whats under the radical
• b2 4ac
• This piece is called the discriminant.

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WHY IS THE DISCRIMINANT IMPORTANT?

• The discriminant tells you the number and types
  of answers
• (roots) you will get. The discriminant can be ,
  , or 0
• which actually tells you a lot! Since the
  discriminant is
• under a radical, think about what it means if you
  have a
• positive or negative number or 0 under the
  radical.

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WHAT THE DISCRIMINANT TELLS YOU!
Value of the Discriminant Nature of the Solutions
Negative 2 imaginary solutions
Zero 1 Real Solution
Positive perfect square 2 Reals- Rational
Positive non-perfect square 2 Reals- Irrational
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Example 1
Find the value of the discriminant and describe
the nature of the roots (real,imaginary,
rational, irrational) of each quadratic equation.
Then solve the equation using the quadratic
formula) 1.
a2, b7, c-11
Discriminant
Value of discriminant137 Positive-NON perfect
square Nature of the Roots 2 Reals - Irrational
Discriminant
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Example 1- continued
Solve using the Quadratic Formula
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Solving Quadratic Equations by the Quadratic
Formula
Try the following examples. Do your work on your
paper and then check your answers.
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Sum and Product of Roots
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Sum Product of Roots
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Write a Quadratic Equation-Ex.1
Write a quadratic equation that has roots
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Write a Quadratic Equation Ex. 2
Write a quadratic equation that has roots
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Solve each equation. Check using sum and
product of the roots.
It CHECKS !
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Write a quadratic equation whose roots satisfy
the following conditions.
You must change the denominators to common
denominators.
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Solve the following quadratic equations and
check using the sum and products of the roots!