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Quadratic Equations
A quadratic equation can be written ax^2 + bx + c = 0 with a not 0. The highest power of x is 2. 3x+2=0 is linear, not quadratic. Collect every term on one side so the other side is 0 before you name a, b, c.
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Quadratic Equations
What is it?
A quadratic equation can be written ax^2 + bx + c = 0 with a not 0. The highest power of x is 2. 3x+2=0 is linear, not quadratic. Collect every term on one side so the other side is 0 before you name a, b, c.
In simple words
- A quadratic equation can be written ax^2 + bx + c = 0 with a not 0.
- WHAT COUNTS: x^2 - 4 = 0 is quadratic (b=0).
- COEFFICIENTS: In 3x2 - 7x + 2 = 0, a=3, b=-7, c=2.
- Worked-method reminder: a = 2, b = 0, c = -8
Important terms
QUADRATIC EQUATIONS: A quadratic equation can be written ax^2 + bx + c = 0 with a not 0. The highest power of x is 2. 3x+2=0 is linear, not quadratic. Collect every term on one side so the other side is 0 before you name a, b, c.
WHAT COUNTS: x^2 - 4 = 0 is quadratic (b=0). 5x^2 + x = 0 is quadratic (c=0). 2x^2 = 8 is quadratic after 2x^2 - 8 = 0. 3x+2=0 is not.
COEFFICIENTS: In 3x^2 - 7x + 2 = 0, a=3, b=-7, c=2. The sign is part of b. Leading coefficient is a, not the last number.
What you should learn
- Explain quadratic equations using the correct definitions, conditions, and notation.
- Apply ax^2 + bx + c = 0, a != 0 correctly in routine and exam-style questions.
- Show each important step, simplify the result, and check that it satisfies the original conditions.
Examples
- x2-4=0
- 2x2=8
- 3x+2=0 is linear
WHAT COUNTS
x^2 - 4 = 0 is quadratic (b=0). 5x^2 + x = 0 is quadratic (c=0). 2x^2 = 8 is quadratic after 2x^2 - 8 = 0. 3x+2=0 is not.
COEFFICIENTS
In 3x^2 - 7x + 2 = 0, a=3, b=-7, c=2. The sign is part of b. Leading coefficient is a, not the last number.
Recommended for Class 10
Full school-level explanation
A quadratic equation can be written ax^2 + bx + c = 0 with a not 0. The highest power of x is 2. 3x+2=0 is linear, not quadratic. Collect every term on one side so the other side is 0 before you name a, b, c.
Recognise it, then name a, b, c:
WHAT — QUADRATIC EQUATIONS
A quadratic equation can be written ax^2 + bx + c = 0 with a not 0. The highest power of x is 2. 3x+2=0 is linear, not quadratic. Collect every term on one side so the other side is 0 before you name a, b, c. The symbols and conditions are part of the mathematics, so include them when stating the rule.
WHY — Why this topic matters
Quadratic Equations matters because quadratic equations model areas, motion, and many algebraic relationships. Knowing more than one solution method lets you choose the quickest reliable method and check the nature of the roots.
HOW — How to solve and explain it
Start by identifying what is given and what must be found. Work through WHAT COUNTS, then COEFFICIENTS. Worked: write 2x^2 = 8 in standard form and name a, b, c. 2x^2 = 8 2x^2 - 8 = 0 a = 2, b = 0, c = -8 Finish by checking signs, restrictions, units, and whether the answer matches the question.
WHAT COUNTS
x^2 - 4 = 0 is quadratic (b=0). 5x^2 + x = 0 is quadratic (c=0). 2x^2 = 8 is quadratic after 2x^2 - 8 = 0. 3x+2=0 is not.
Remember
- degree 2
Examples
- x2-4=0
- 2x2=8
- 3x+2=0 is linear
COEFFICIENTS
In 3x^2 - 7x + 2 = 0, a=3, b=-7, c=2. The sign is part of b. Leading coefficient is a, not the last number.
Remember
- a is x^2
Examples
- a=3, b=-7, c=2
- x2+6x+9: a=1,b=6,c=9
- Do not swap a and c
Remember
- ax2 + bx + c = 0
- a != 0
- a=2, b=0, c=-8
- a not zero
- degree 2
- a is x^2
- ax2 + bx + c = 0
- a != 0
How the ideas connect
Worked: write 2x^2 = 8 in standard form and name a, b, c. 2x^2 = 8 2x^2 - 8 = 0 a = 2, b = 0, c = -8
Deeper understanding
Go beyond memorising Quadratic Equations. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked: write 2x^2 = 8 in standard form and name a, b, c. 2x^2 = 8 2x^2 - 8 = 0 a = 2, b = 0, c = -8
Common mistakes
Exam focus
Core Idea
WHAT COUNTS
COEFFICIENTS
Worked Method
Exam focus
Quick revision
- ax2 + bx + c = 0
- a != 0
- a=2, b=0, c=-8
- a not zero
- QUADRATIC EQUATIONS: A quadratic equation can be written ax^2 + bx + c = 0 with a not 0. The highest power of x is 2. 3x+
- WHAT COUNTS: x^2 - 4 = 0 is quadratic (b=0). 5x^2 + x = 0 is quadratic (c=0). 2x^2 = 8 is quadratic after 2x^2 -
If a = 0 the equation is no longer quadratic. The x^2 term must actually be there.
For long answers on Quadratic Equations: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- ax2 + bx + c = 0
- a != 0
- a=2, b=0, c=-8
- a not zero
Important formulas
- ax2 + bx + c = 0
- a != 0
- a=2, b=0, c=-8
Common exam traps
- If a = 0 the equation is no longer quadratic. The x^2 term must actually be there.
- Do not swap a and c
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
If a = 0 the equation is no longer quadratic. The x^2 term must actually be there.
- Mistake
Do not swap a and c
- Mistake
Do not treat WHAT COUNTS and COEFFICIENTS as the same step; each has a different purpose.
- Mistake
If a = 0 the equation is no longer quadratic. The x^2 term must actually be there.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
ax2 + bx + c = 0
a != 0
a=2, b=0, c=-8
a not zero
A quadratic equation can be written ax^2 + bx + c = 0 with a not 0. The highest power of x is 2. 3x+2=0 is linear, not quadratic. Collect every term on one side
ax2 + bx + c = 0
- Definition
- A quadratic equation can be written ax^2 + bx + c = 0 with a not 0. The highest power of x is 2. 3x+2=0 is linear, not quadratic. Collect every term on one side
- Formula
- ax2 + bx + c = 0
- Example
- x2-4=0
- Critical warning
- If a = 0 the equation is no longer quadratic. The x^2 term must actually be there.
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Exam Practice
Define
Q1. Define Quadratic Equations.
Explain
Q2. Explain: WHAT COUNTS.
Example
Q3. Give one clear example of Quadratic Equations and say why it fits.
Mistake
Q4. State one common mistake students make about Quadratic Equations.
Exam note
Q5. Write a short exam note on Quadratic Equations: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.