Class 10 · Maths

Quadratic Equations

A quadratic equation in x is an equation of the form ax² + bx + c = 0, where a ≠ 0. This chapter covers checking quadratic equations and solving them.

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Exercise 4.1

Q1. Exercise 4.1 — Question 1

Check whether (x + 1)² = 2(x − 3) is a quadratic equation.

Expand the left side: x² + 2x + 1. Right side: 2x − 6. Bring all terms to one side: x² + 2x + 1 − 2x + 6 = 0, i.e. x² + 7 = 0. Since the highest power of x is 2, it is a quadratic equation.

Formula: Standard form: ax² + bx + c = 0, a ≠ 0

Final Answer: Yes, it is a quadratic equation (x² + 7 = 0).

Common Mistake: Forgetting to move every term to one side before checking the degree.

Exam Tip: Always simplify to standard form first.

Q2. Exercise 4.1 — Question 2

Represent the situation: the product of two consecutive positive integers is 306.

Let the smaller integer be x, so the next is x + 1. Their product: x(x + 1) = 306, i.e. x² + x − 306 = 0. This is the required quadratic equation.

Final Answer: x² + x − 306 = 0

Common Mistake: Writing the integers as x and x + 2 instead of x and x + 1.

Exam Tip: Define the variable clearly before forming the equation.

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