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Friday 3rd of July Home Square Roots and Radical Expressions Solving Radical Equations Simplifying Radical Expressions Irrational Numbers in General and Square Roots in Particular Roots of Polynomials Simplifying Radical Expressions Exponents and Radicals Products and Quotients Involving Radicals Roots of Quadratic Equations Radical Expressions Radicals and Rational Exponents Find Square Roots and Compare Real Numbers Radicals Radicals and Rational Exponents Theorems on the Roots of Polynomial Equations SYNTHETIC DIVISION AND BOUNDS ON ROOTS Simplifying Radical Expressions Exponents and Radicals Properties of Exponents and Square Roots Solving Radical Equations Rational Exponents and Radicals,Rationalizing Denominators Rational Exponents and Radicals,Rationalizing Denominators Quadratic Roots Exponents and Roots Multiplying Radical Expressions Exponents and Radicals Solving Radical Equations Solving Quadratic Equations by Factoring and Extracting Roots Newton's Method for Finding Roots Roots of Quadratic Equations Studio Roots, Radicals, and Root Functions Review division factoring and Root Finding Radicals Simplifying Radical Expressions Multiplying and Simplifying Radical Expressions LIKE RADICALS Multiplication and Division of Radicals Radical Equations BOUNDING ROOTS OF POLYNOMIALS
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I. Finding Roots of Quadratic Equations
a. The Standard Form of a quadratic equation is: ax2 + bx + c = 0 .
b. We can use the Quadratic Formula to solve equations in standard
form: c. Discriminant – The radical portion of this formula sqrt(b2 − 4ac) ,
determines the nature of the roots. This quantity under the radical
sign b2 − 4ac , is called the discriminant. d. Three things may occur regarding the discriminant:

i. If b2 − 4ac > 0
We can take the square root of this positive amount
and there will be two different real answers (or roots)
to the equation.

ii. If b2 − 4ac < 0
We cannot take the square root of a negative number,
so there will be no real roots.

iii. If b2 − 4ac = 0
The amount under the radical is zero and since the
square root of zero is zero, we will get only 1 distinct
real root.

II. Examples   III. Practice Problems
By examining the discriminant = b2 − 4ac , determine how many real
roots, if any, the following quadratic equations have.

1. x2 − 4x + 4 = 0

2. x2 + 4 = 0

3. x2 − 2x + 4 = 0

4. x2 − 4x = 0

5. 5r2 − 3r + 2 = 0

6. 7x2 −10x − 5 = 0

7. x2 − 4 = 0

8. 25t2 −10t = −1

9. 6y2 − 5y = 21

10. 2y2 −19y = 3