Try These
2 Solve for x.
1 What are the roots of each factored
(a)
(b)
(c)
(d)
(e)
(f)
quadratic?
(a) n(n - 4) = 0
(b) (m + 2)(m + 2) = 0
(c) 5(k+1)(k-1)=0
(d) 4t(t - 7) = 0
(e) (2d-1)(d-3)=0
(f) (a + 4)(3a - 2) = 0
(x + 1)(x
(x + 3)(x
(x - 2)(x
(x - 6)(x
(x - 2)(x
(x - 3)(x
+ 2) =
+ 5) =
+ 1) =
+ 5) =
+ 2) =
+ 8) =
0
0
0
0
0
0
'j
)
)
Written Exercises
B
A Remember: Use the principle to solve quadratic
equations.If ab = 0 then either a = 0 or b = 00
/r
fIr
,
1 Solve by factoring. Check your results.
(a) x2+ 3x + 2 = 0
(b) x2 - 6x - 7 = 0
(c) x2- X- 2 = 0
(d) x2 - 6x + 5 = 0
(e) x2 -
5x
+6
= 0
(f)
x2 + 2x - 3 = 0
2 Solve and verify.
Remember to check for
any common factors first.
(a) ni2 -'25 = 0
1'..
~
(c)3?r,3x -C..
'
\...
'-6 = 0
(e) 4p2 - 28p = 0
(b) y2 + 6y = 0
(d) n2 + 8n - 33 = 0
(f) 2f2 - 6f - 20 = 0
3 Factor. Then find the roots.
(a) x2+ 9x +
~=
0
(b) a2 - 3a + 2 = 0
(d) m2 - 2m - 8 = 0
(c) p2 - 36 = 0
(e) (2-(-60=0
(g) x2- 4x - 21 = 0
(f) y2-2y-15=0
(h) x2 - x - 42 = 0
4 (a) Solve and check.
x2
+ 6x + 9 =
Find the roots. Verify your answers.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
x2 + 2x+ 1 = 0
a2 - 4a - 12 = 0
d2 + 3d - 10 = 0
m2-8m+12=O
t2- 8t + 16 = 0
6q2 - 3q = 0
az + 8a + 15 = 0
2x2 + 10x + 8 = 0
~ Solve
and check.
(a) 3\if-12w-36=0
(b)
(c)
(d)
(e)
(f)
(g)
4y2 + 28y - 72 = 0
2p2 + 10p + 8 = 0
3x2_12x-63=0
5k2 - 10k - 40 = 0
3a2 - 6a + 3 = 0
3h2 - 12 = 0
(h) 4m2- 8m + 4 = 0
0
(b) How many roots did you find in (a)?
(c) How are these roots related?
!
\
Once you factor the equation, check your
factors. Remember to look for common factors
first.
5 (a) Solve and check.
x2-9=0
(b) How many roots did you find in (a)?
(q) How are the roots related?
8 A jewelry company finds that the best size of
cardboard on which to market its earrings is
given by the roots of the equation
x2-14x+48=O
where x is the length of a side measured in
centimetres. Find the dimensions of the
cardboard.
\-0-7
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