Knowledge organisers

Quadratic Equations: CBSE Class 10 Maths knowledge organiser

Everything to know about quadratic equations on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Quadratic equation: An equation ax² + bx + c = 0 with a ≠ 0.
Discriminant: D = b² − 4ac decides the nature of the roots.
Root: A value of x that satisfies the equation.

Key formulas

\(ax^2+bx+c=0,\ a\ne0\)	\(x=\frac{-b\pm\sqrt D}{2a},\) \(D=b^2-4ac\)
Nature of roots	\(D>0\text{ two distinct real};\) \(D=0\text{ two equal real }\big(x=-\tfrac b{2a}\big);\) \(D<0\text{ no real roots}\)

Worked example

Solve \(x^2 + 2x - 4 = 0\): \(D = 4 + 16 = 20\), \(x = \dfrac{-2 \pm 2\sqrt5}{2} = -1 \pm \sqrt5\).

Common mistakes

Dividing both sides by \(x\) and losing the root \(x = 0\).
Using \(b\) instead of \(-b\) in the formula, or dividing only the root term by \(2a\).
Forgetting to rearrange to “\(= 0\)” before factorising.
Not rejecting inadmissible roots in word problems.

You should be able to…

Recognise a quadratic, solve it by factorisation or the formula and find the discriminant.
Decide the nature of the roots, find k for equal or real roots and set up quadratic word problems from speed, area and number situations.
Write full-marks 5-mark word problems: equation formed, solved, the impossible root rejected with a reason, answer in context.
Handle surd coefficients, rational equations and 'for every value of m' discriminant proofs.

The printable sheet

Quadratic Equations knowledge organiser for CBSE Class 10 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Quadratic Equations knowledge organiser (CBSE Class 10 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 10 Maths topics: Real Numbers · Polynomials · Pair of Linear Equations in Two Variables · Arithmetic Progressions · Triangles · Coordinate Geometry · Introduction to Trigonometry · Some Applications of Trigonometry · Circles · Areas Related to Circles · Surface Areas and Volumes · Statistics · Probability · All CBSE Class 10 Maths organisers