L M
earn
aths
MATHEMATICS
For
GCSE
QUADRATIC FORMULA
GCSE Higher Tier
Also
KS3 Top set
Denis Dalaba MSc, B.Ed.
www.maths4maths.co.uk by D. Dalaba
1
The quadratic formula
Introduction
Quadratic equations can also be solved using the quadratic
formula.
The formula is
The formula is used to work out the solutions of a standard
quadratic of the form
Where a, b and c are rational numbers with a ≠ 0.
When I was in secondary school we used to call this formula
‘The almighty quadratic formula’
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2
Identification of the values to use for a, b, c
Example
Identify the values of a, b, c for each of the quadratic
equations for use with the quadratic formula.
1) 7x2 + 22x + 3 = 0
5) 3x + 7 + 2x2 = 0
a=
a=
b=
c=
2) 2x2 – 3x -10 = 0
a=
b=
b=
c=
b=
a=
b=
c=
7) - x2 + x + 2 = 0
c=
4) x2 - 9x = 0
a=
c=
6) x2 - x = 6
3) 5x2 + x – 6 = 0
a=
b=
a=
b=
c=
8) x2 = 4x + 1
c=
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a=
b=
c=
3
Example 1
Use the quadratic formula to solve the equation
x2 + 9x + 14 = 0
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4
Example 2
Use the formula to solve the equation
3x2 – 2x - 5 = 0
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Example 3
Use the formula to solve the equation.
Give your answers correct to 3 decimal places.
5x2 + x = 7
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Example 4
4x2 – 20x + 25 = 0
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Example 5
(6x + 5)x = -1
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What is the quadratic equations?
A. Given a solution
A quadratic equation has x = 2 and x = 3 as it
solutions,
What is the quadratic equation?
B.
Given a formula
A substitution into a quadratic formula gave
What is the quadratic equation?
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Completing the square
Quadratic equations can also be solved using
completing the square
(i) Solve using completing the square
x2 + 9x + 14 = 0
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(ii) Solve using completing the square
2x2 + 7x + 3 = 0
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11
Deriving the quadratic formula
Completing the square is used to derive the
quadratic formula
ax2 + bx + c = 0
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