Knowledge organisers

Polynomials: CBSE Class 10 Maths knowledge organiser

Everything to know about polynomials 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

Zero of a polynomial: A value of x that makes p(x) = 0; on a graph, where the curve meets the x-axis.
Quadratic polynomial: A polynomial of degree 2: ax² + bx + c with a ≠ 0.
Sum and product of zeroes: For ax² + bx + c, α + β = −b/a and αβ = c/a.

Key formulas

Zeroes \(\alpha,\beta\) of \(ax^2+bx+c\)	\(\alpha+\beta=-\frac ba,\) \(\alpha\beta=\frac ca\)
Quadratic with zeroes \(\alpha,\beta\)	\(k\big[x^2-(\alpha+\beta)x+\alpha\beta\big]\)
Zeroes of \(p(x)\) = \(x\)-coordinates where \(y=p(x)\) meets the \(x\)-axis; degree \(n\) ⇒ at most \(n\) zeroes

Worked example

Zeroes of \(3x^2 + 5x - 2\): split \(-6 = 6 \times (-1)\): \(3x^2 + 6x - x - 2 = (3x - 1)(x + 2)\). Zeroes \(\dfrac13, -2\). Check: sum \(-\dfrac53 = -\dfrac{b}{a}\), product \(-\dfrac23 = \dfrac{c}{a}\).

Common mistakes

Sign slip: the sum of zeroes is \(-b/a\), not \(b/a\).
Writing \(x^2 + Sx + P\) instead of \(x^2 - Sx + P\).
Stating that a quadratic “has exactly 2 zeroes” — it may have 0, 1 or 2 real zeroes.
When verifying the relationship, forgetting to compare with \(-b/a\) and \(c/a\) explicitly.

You should be able to…

Find the zeroes of a quadratic by splitting the middle term and read the number of zeroes from a graph.
Use sum = −b/a and product = c/a confidently, verify the relationship, and build a quadratic from given zeroes.
Write full-marks long answers and case studies, including completing a table, plotting the graph and reading off the zeroes.
Handle expressions like α² + β² or α/β + β/α without solving, and build new polynomials whose zeroes are changed versions of old ones.

The printable sheet

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

Revise it next

Other CBSE Class 10 Maths topics: Real Numbers · Pair of Linear Equations in Two Variables · Quadratic Equations · 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