Quadratic Equation - Class 10 Chapter 4 Short Notes (Mind Maps)

The quadratic formula is x = (−b ± √(b² − 4ac)) / 2a. Use it when the equation cannot be factorised easily — especially when roots are irrational (e.g., 2 ± √3). It always works for any quadratic equation and is the safest method in timed exam conditions.

Calculate the discriminant D = b² − 4ac. If D > 0, the equation has two distinct real roots. If D = 0, it has two equal real roots. If D < 0, it has no real roots. This method is faster than solving and is directly tested in CBSE board exams.

The standard form is ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. Here, a is the coefficient of x², b is the coefficient of x, and c is the constant. This form is the starting point for all solving methods taught in CBSE Class 10 Chapter 4.

For the equation ax² + bx + c = 0 with roots α and β: the sum of roots α + β = −b/a and the product of roots αβ = c/a. These relationships allow you to form a new quadratic equation when roots are given, using: x² − (sum)x + (product) = 0.

A quadratic equation ax² + bx + c = 0 has real roots when its discriminant is D ≥ 0, meaning b² − 4ac ≥ 0. If b² − 4ac < 0, the equation has no real roots. This condition is commonly tested in CBSE with "find the value of k" problems

No. By the Fundamental Theorem of Algebra, a polynomial of degree 2 has exactly 2 roots (counting multiplicity). A quadratic equation cannot have three or more roots. If D = 0, both roots are equal, so there is effectively one unique value — but it counts as a repeated root.