Teaching Notes 5.21: Solving Quadratic Equations
by Finding Square Roots
Solving quadratic equations by finding square roots involves a basic understanding of square
roots. Students may forget that positive numbers have two square roots, zero has one square root,
and negative numbers have no real square roots.
- Discuss the concept of squares and square roots with your students. Ask them what number
multiplied by itself equals 9. Most students will say 3×3, which is correct. Be sure to note
that− 3 ×−3 also equals 9. Both examples may be expressed asx^2 =9. - Explain that because 9 is a positive number,x^2 =9 has two solutions. The two solutions
arex=±
√
9, which meansx=3andx=−3. Emphasize that the symbol±is read ‘‘plus
or minus’’ and denotes both the positive and negative square roots.
- Present additional examples. Ask your students what number multiplied by itself equals 0.
There is only one solution,x=0. Ask them what number multiplied by itself equals−49.
There is no real solution, because no real number multiplied by itself is equal to−49. (You
might want to mention that there are solutions for negative numbers in the imaginary
numbers.) - Review the information and example on the worksheet with your students. Note that stu-
dents must isolate the squared term on one side of the equation before they can find the
square root.
EXTRA HELP:
This method for solving quadratic equations by finding square roots cannot be used if there is anx
term in the equation.
ANSWER KEY:
(1)x=11 andx=− 11 (2)x=10 andx=− 10 (3)x=1andx=− 1 (4)x= 0
(5)No real solutions (6)x=7andx=− 7 (7)x= 0 (8)No real solutions
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(Challenge)Deanna rewrote the problem incorrectly. She should have subtracted 16 from
both sides of the equation and writtenx^2 =−16. When she substituted her answers in an
incorrect equation they checked. The answers would not have checked if she had substituted
them in the original equation.
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216 THE ALGEBRA TEACHER’S GUIDE