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Mathematics · Class 9 · Chapter 8: Quadratic Equation

8 min

Key points

A quadratic equation is an equation of the form ax² + bx + c = 0, where a ≠ 0
The general form ax² + bx + c = 0 has three methods of solution: factorization, completing the square, and quadratic formula
The discriminant Δ = b² - 4ac determines the nature of roots
If Δ > 0, roots are real and distinct; if Δ = 0, roots are real and equal; if Δ < 0, roots are imaginary
Sum of roots = -b/a and Product of roots = c/a
Completing the square method converts ax² + bx + c = 0 into perfect square form
Quadratic formula: x = (-b ± √(b² - 4ac))/2a gives roots directly
Word problems involving quadratic equations often relate to area, age, and number problems

Definitions

Quadratic Equation: An equation of the form ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0, is called a quadratic equation in one variable x.
Discriminant: The expression b² - 4ac under the square root in the quadratic formula is called the discriminant of the quadratic equation ax² + bx + c = 0.
Roots of Quadratic Equation: The values of x which satisfy the quadratic equation ax² + bx + c = 0 are called the roots or solutions of the equation.
Completing the Square: The method of solving quadratic equation by converting it into perfect square form is called completing the square method.

Worked example

Solve the quadratic equation 2x² - 7x + 3 = 0 using quadratic formula. (6 marks)

The roots are x = 3 and x = 1/2

Common mistakes

Students forget to check if a ≠ 0 when identifying quadratic equations
Wrong calculation of discriminant - especially sign errors with negative coefficients
Not writing ± symbol when taking square root in completing the square method
Forgetting to verify answers by substituting back into original equation
Confusing sum and product of roots formulas (writing -c/a instead of c/a for product)

Quick recap

A quadratic equation has standard form ax² + bx + c = 0 where a ≠ 0. It can be solved by factorization, completing square, or quadratic formula x = [-b ± √(b² - 4ac)] / 2a. The discriminant b² - 4ac determines nature of roots: positive gives real unequal roots, zero gives real equal roots, negative gives complex roots. Always identify coefficients first and show all calculation steps for full marks.

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