ALL EXPERIMENTS
NCERT · Class 10 · Chapter 4

Quadratic Equations
on the drafting table

Every idea in this chapter — standard form, real‑world modelling, factorisation, and the discriminant — drawn out like a blueprint. Turn the dials, split the middle term, and watch the parabola respond.

4.2 · Recognising the standard form

A quadratic equation can be written as ax² + bx + c = 0, a ≠ 0 — but it doesn't always arrive looking that tidy. Simplify each card first, then click it to check your answer.

Quadratic Not quadratic

4.1 · Modelling the prayer hall

A charity trust wants a hall with carpet area 300 m², its length one metre more than twice its breadth. Drag the breadth and watch the plan — and the equation — respond.

Breadth (x)
6 m
Length (2x+1)
13 m
Area = x(2x+1)
78 m²
Target area
300 m²
Keep sliding — the area needs to reach exactly 300 m².
Area equation: 2x² + x = 300  →  standard form 2x² + x − 300 = 0
Factorising: (x − 12)(2x + 25) = 0 → x = 12 or x = −12.5
Since a breadth can't be negative, breadth = 12 m, length = 25 m.

4.3 · Solving by factorisation

Split the middle term bx into two parts whose product is ac and whose sum is b, then factor by grouping. Pick a textbook example or try your own integers.

4.4 · Discriminant, roots & the quadratic formula

The sign of b² − 4ac decides everything. Adjust a, b and c and watch the parabola, its roots, and the formula update together.

discriminant b² − 4ac =
x = ( −b ± √(b²−4ac) ) / 2a