INTERMEDIATE ALGEBRA
CH 03 SEC 3 HW WORKSHEET
1. Solve
2. Solve
3. Solve
4. Solve
5. Solve
pg. 1
math
hands
Solving
equations w/radicals
q
6x2 + 4x = 4
q
2x2 + 5x = 5
q
3x2 + 2x = 1
q
6x2 + 5x = 5
q
6x2 + 5x = − 5
c
2007-2011
MathHands.com v.1010
INTERMEDIATE ALGEBRA
CH 03 SEC 3 HW WORKSHEET
6. Solve
7. Solve
8. Solve
9. Solve
10. Solve
pg. 2
math
hands
Solving
equations w/radicals
q
2x2 − 5x = − 5
q
15x2 + 6x = − 3
q
q
3
15x2 − 10x = 3 25
q
q
3
6x2 + 7x = 3 49
q
q
3
7x2 + 30x = 3 25
c
2007-2011
MathHands.com v.1010
INTERMEDIATE ALGEBRA
CH 03 SEC 3 HW WORKSHEET
11. Solve
math
hands
q
− 2 + 2 2x + 1 = 3x
12. Solve
5+3
13. Solve
14. Solve
15. Solve
pg. 3
Solving
equations w/radicals
q
2x − 1 = 3x
q
q
2x − 1 = 5x + 3
q
q
x − 2 = 3x + 1
q
q
5x − 2 = 2x + 7
c
2007-2011
MathHands.com v.1010
INTERMEDIATE ALGEBRA
CH 03 SEC 3 HW WORKSHEET
16. Solve
pg. 4
math
hands
Solving
equations w/radicals
q
q
5x − 2 = 3x + 1
c
2007-2011
MathHands.com v.1010
INTERMEDIATE ALGEBRA
Solving
equations w/radicals
math
hands
CH 03 SEC 3 NOTES
THE IDEA
In this section we consider equations containing radicals. The general strategy will be to isolate the term containing
a radical, then square [or higher power] both sides of the equation. Often, this annihilates the radical and yields
a polynomial equation. From that point, one can use the skills and tools of polynomial equations. If the equation
has more than one term with a radical, one can annihilate one radical at a time by isolating it, then squaring both
sides, then repeating the process for other radicals that were not isolated and annihilated. As before, caution is
advised since squaring both sides [or raising both sides to an power > 2] can, and often does, introduce extraneous
solutions. Solutions, should be checked at the end.
EXAMPLES Solving equations with radical/s:
Solve
q
2x2 − 3x = 3
Solutions:
q
2x2 − 3x = 3
2
q
2
2
2x − 3x = 3
(SBST)
2x2 − 3x = 9
(def of Rad, BI)
2x − 3x − 9 = 0
(2x + 3)(x − 3) = 0
(BI)
(BI)
2
2x + 3 = 0
3
x= −
2
pg. 5
(given)
OR
OR
x−3=0
(ZFT)
x=3
(ZFT)
c
2007-2011
MathHands.com v.1010