Solving Quadratic Equations By Using The Quadratic Formula Worksheet With Answers (Page 30 of 41) in pdf

Solving Quadratic Equations By Using The Quadratic Formula Worksheet With Answers Page 30

The solutions are 12.9 and 0.7.

c. The margins should be about 0.7 in. on the sides, 4 • 0.7 = 2.8 in. on the top, and 3 • 0.7 = 2.1 in. on the bottom.

50. MULTIPLE REPRESENTATIONS In this problem, you will investigate writing a quadratic equation with given

9-5 Solving Quadratic Equations by Using the Quadratic Formula

roots.

If p is a root of 0 = ax

+ bx + c, then (x – p ) is a factor of ax

+ bx + c.

a. Tabular Copy and complete the first two columns of the table.

b. Algebraic Multiply the factors to write each equation with integral coefficients. Use the equations to complete

the last column of the table. Write each equation.

c. Analytical How could you write an equation with three roots? Test your conjecture by writing an equation with

roots 1, 2, and 3. Is the equation quadratic? Explain.

SOLUTION:

a . For any two roots m and p , in the left hand column, the middle column will be the corresponding factors (x

–

m), (x

–

p ).

b . The equation with these factors will be: (x

–

m)(x

–

p ) = 0 which simplifies to x

– (m + p )x + mp = 0. Use this to

fill in the column of the table.

c . You could write an equation with three roots by multiplying the corresponding factors together and setting it equal

– 1), (x – 2), and (x –

to zero. If an equation has the three roots 1, 2, 3, then the corresponding factors would be (x

3). The equation would then be:

eSolutions Manual - Powered by Cognero

Page 30

This is not a quadratic equation since it is of degree 3.

Solving Quadratic Equations By Using The Quadratic Formula Worksheet With Answers Page 30