Solving Quadratic Equations From Their Factors (1)

In this worksheet, students solve quadratic equations from their factorised form.

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Solve Quadratic Equations by Factorising

Difficulty level:

QUESTION 1 of 10

A quadratic expression can sometimes be factorised.  If the product of these factors is zero, it is easy to solve the associated quadratic equation.

We use the fact that, if ab = 0, then we know that either a = 0 or b = 0 (or both).

Example

Solve for x:

(x + 3) (x - 5) = 0

If (x + 3) (x - 5) = 0

then either (x + 3) = 0 or (x - 5) = 0

Write each equation separately.

x + 3 = 0                                         x - 5 = 0

Subtract 3 from both sides.                      Add 5 to both sides.

x + 3 - 3 = 0 - 3                              x - 5 + 5 = 0 + 5

Simplify.

x = -3                                             x = 5

Solution is:

x = -3 or x = 5

Solve the quadratic equation by selecting all the correct solutions below.

(x + 6) (x - 6) = 0

x = -18

x = -6

x = 18

x = 6

Solve the quadratic equation by selecting all the correct solutions below.

(x + 3) (x - 4) = 0

x = 3

x = -3

x = -4

x = 4

Solve the quadratic equation by selecting all the correct solutions below.

(x + 7) (x + 4) = 0

x = -4

x = 4

x = 7

x = -7

Solve the quadratic equation by selecting all the correct solutions below.

(x) (x + 1) = 0

x = 1

x = ½

x = -1

x = 0

Solve the quadratic equation by selecting all the correct solutions below.

(x + 8) (x - 1) = 0

x = 1

x = -8

x = -1

x = 8

Solve the quadratic equation by selecting all the correct solutions below.

(x + 3) (x + 3) = 0

x = 9

x = -9

x = -3

x = 3

Solve the quadratic equation by selecting all the correct solutions below.

(x - 6) (x - 5) = 0

x = 5

x = -5

x = -6

x = 6

Solve the quadratic equation by selecting all the correct solutions below.

(x + 3) (x - 3) = 0

x = -3

x = 3

x = 9

x = -9

Solve the quadratic equation by selecting all the correct solutions below.

(x + 4) (x - 7) = 0

x = -4

x = 7

x = 4

x = -7

Solve the quadratic equation by selecting all the correct solutions below.

(x + 10) (x - 100) = 0

x = 100

x = 10

x = -10

x = -100

• Question 1

Solve the quadratic equation by selecting all the correct solutions below.

(x + 6) (x - 6) = 0

x = -6
x = 6
• Question 2

Solve the quadratic equation by selecting all the correct solutions below.

(x + 3) (x - 4) = 0

x = -3
x = 4
• Question 3

Solve the quadratic equation by selecting all the correct solutions below.

(x + 7) (x + 4) = 0

x = -4
x = -7
• Question 4

Solve the quadratic equation by selecting all the correct solutions below.

(x) (x + 1) = 0

x = -1
x = 0
• Question 5

Solve the quadratic equation by selecting all the correct solutions below.

(x + 8) (x - 1) = 0

x = 1
x = -8
• Question 6

Solve the quadratic equation by selecting all the correct solutions below.

(x + 3) (x + 3) = 0

x = -3
• Question 7

Solve the quadratic equation by selecting all the correct solutions below.

(x - 6) (x - 5) = 0

x = 5
x = 6
• Question 8

Solve the quadratic equation by selecting all the correct solutions below.

(x + 3) (x - 3) = 0

x = -3
x = 3
• Question 9

Solve the quadratic equation by selecting all the correct solutions below.

(x + 4) (x - 7) = 0

x = -4
x = 7
• Question 10

Solve the quadratic equation by selecting all the correct solutions below.

(x + 10) (x - 100) = 0