Class 10 / Maths
Class 10 Maths Quadratic Equations Notes
Exam-focused notes on standard form, roots, factorization, and checking solutions.
Topic introduction
Quadratic equations are equations where the highest power of the variable is 2. The chapter becomes easier when every question is first converted into standard form and the solving method is chosen carefully.
Key points
- A quadratic equation has standard form ax^2 + bx + c = 0, where a is not zero.
- Roots are values of x that satisfy the equation.
- Factorization works when the middle term can be split suitably.
Definitions
Quadratic equation: An equation of the form ax^2 + bx + c = 0, where a is not equal to zero.
Root: A value of x that satisfies the equation.
Discriminant: The value b^2 - 4ac, used to identify the nature of roots.
Formulas
- Standard form: ax^2 + bx + c = 0
- Quadratic formula: x = (-b +/- sqrt(b^2 - 4ac)) / 2a
- Discriminant: D = b^2 - 4ac
Examples
- x^2 - 7x + 12 = 0 becomes (x - 3)(x - 4) = 0, so x = 3 or x = 4.
- For 2x^2 + 3x - 2 = 0, a = 2, b = 3, c = -2.
- If D = 0, the quadratic equation has two equal real roots.
Standard form
Always arrange the equation into ax^2 + bx + c = 0 before solving.
Check signs carefully because sign errors are common in factorization.
Checking roots
After finding roots, substitute each value into the original equation.
A correct root should make the left side equal to zero.
Common mistakes
- Forgetting that a cannot be zero in a quadratic equation.
- Changing signs incorrectly while moving terms to standard form.
- Stopping after factorisation without writing final roots.
Quick practice
- Solve x^2 - 7x + 12 = 0.
- Write the standard form of x^2 = 5x - 6.
- Check whether x = 2 is a root of x^2 - 3x + 2.
Related practice
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