9.1c S KM & PP 1

Quadratic Equations02 cbxax

9.1c S KM & PP 2

Square Roots:Know Your Squares!

Consider this equation:

492 xWhat number(s) could be squared

to give a result of 49?From our knowledge of number facts,

we would know that the answer would be:7x 7xbecause

497 2 497 2 77,

9.1c S KM & PP 3

Square Roots:Know how to factor!

492 x

07 x 07 x

We could also put the equation in STANDARD FORM and factor to find

the solutions.

0492 x

7x 7x 77,

077 xx

9.1c S KM & PP 4

Square Roots:Know the Rules!

492 xBecause this equation has the form:BINOMIAL SQUARE equals NUMBER

we can use the SQUARE ROOT PROPERTY!

7x

77,

492 x Remember the + because every positive number has two square roots!

9.1c S KM & PP 5

TheSquare Root Property:

x2 = n and n = 0

02 x has one solution, x = 0.

{0}

9.1c S KM & PP 6

TheSquare Root Property:

x2 = n and n > 0

nx

If n is a positive number, i.e., n > 0 , thennx 2

has two real solutions.

n,n

9.1c S KM & PP 7

TheSquare Root Property:

x2 = n and n < 0

If n is a negative number, i.e., n < 0 , then x2 = n has no Real Solutions.

Ø

9.1c S KM & PP 8

TheSquare Root Property:

Summary

02 x has one solution, x = 0.

nx

If n is a positive number, i.e., n > 0 , thennx 2

has two real solutions.

If n is a negative number, i.e., n < 0 , then x2 = n has no Real Solutions.

9.1c S KM & PP 9

General Strategy forSolving a Quadratic

Equation by taking the Square Root

1)See that the equation only has the quadratic and the constant terms.

2) Solve the equation for the quadratic variable, the squared variable.

3) Take square roots on both sides of the equation and remember to put + before the radical.

4) Simplify the radical.

9.1c S KM & PP 10

Square Root PropertySolve: x2 = 144

1442 x

12x 1212,

144x

12

9.1c S KM & PP 11

Square Root PropertySolve: 2x2 - 100 = 0

502 x

25x 2525 ,

50x

25

2x

25 2

9.1c S KM & PP 12

Square Root PropertySolve: 16x2 -3=0

1632 x

43

x

43

2x

9.1c S KM & PP 13

Square Root PropertySolve: 7x2 -5=0

752 x

75

x

735

2x

77

9.1c S KM & PP 14

Square Root PropertySolve: 2x2 +18=0

92 x

9x

2x

9.1c S KM & PP 15

Square Root PropertySolve: 3x2 + 5 = 5

02 x

0x

0

2x

0

9.1c S KM & PP 16

When the Quadratic Equation is missing the linear term, the term with x1, it is generally a good idea to try the Square Root Property to solve the problem.

is the form best suited to using the Square Root Property.This will be important when we study solving quadratic equations by Completing the Square!

The Square Root Property

( variable expression )2 = #

9.1c S KM & PP 17

That’s All for Now!