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CanadaON
Grade 9

4.05 Simple quadratic equations

Worksheet
Quadratic equations
1

The equation x^{2} - 144 = 0 has a positive integer solution of x = 12. Find its other solution.

2

Solve the following equations:

a

x^{2} = 2

b

x^{2} = 25

c

x^{2} = 121

d

x^{2} = 294

e

x^{2} - 121 = 0

f

x^{2} - 10 = 15

g

\dfrac{x^{2}}{16} - 2 = 2

h

\dfrac{x^{2}}{25} - 3 = 6

i

\left(x + 3\right)^{2} = 49

j

\left(x - 3\right)^{2} = 64

k

\left(x - 6\right)^{2} = 2

l

\left(2 - x\right)^{2} = 81

m

\left(x - 7\right)^{2} = 81

n

\left(7 - x\right)^{2} = 81

o

\left( 8 x + 9\right)^{2} = 256

p

81 x^{2} - 16 = 0

3

Solve the following equations:

a

4 y^{2} = 100

b

25 y^{2} = 36

c

- 3 k^{2} = - 12

d

81 k^{2} + 8 = 24

e

- 25 v^{2} + 64 = 0

f

10 \left(p^{2} - 7\right) = 930

4

Solve the following equation for x, in terms of a and c. Assume a and c are positive.

a x^{2} - c = 0

Applications
5

The equation 4 x^{2} + k x + 16 = 0 has one solution: x = 2. Find the value of the coefficient k.

6

The equation a x^{2} - 32 x - 80=0 has one soulution: x = 4. Find the value of the coefficient of a.

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9.C1.5

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