Class 10 Maths|Chapter 2 -Polynomials|L1 - Geometrical meaning of zeroes|GSEB English Medium 2026-27

Описание: Welcome to Chapter 2 – Polynomials (Lecture 2) of Class 10 Maths GSEB English Medium.
In this lecture, we understand the Geometrical Meaning of Zeroes of a Polynomial using graphs. This concept helps students determine the number of zeroes of a polynomial from its graph.
📚 Topics covered in this lecture:
✔ Geometrical Meaning of Zeroes of Polynomial
✔ Relation between graph of polynomial and zeroes
✔ Number of zeroes from graph
✔ Graph intersecting x-axis
✔ Graph touching x-axis
✔ Linear polynomial graph
✔ Quadratic polynomial graph
✔ Cubic polynomial graph
📊 Board and Previous Year Questions Covered
✔ GSEB Board Questions
✔ MCQ questions based on graphs
✔ Finding number of zeroes from graph
✔ Graph identification questions
This lecture is part of the complete Class 10 Maths GSEB course for 2026–27 board exam preparation.

Questions solved in this video:
• How to find number of zeroes of a polynomial from graph?
• What is geometrical meaning of zeroes?
• How many zeroes can a polynomial have?

📖 Chapter: Polynomials
🎥 Lecture: 2
🏫 Board: GSEB
📘 Class: 10 Maths (English Medium)

Content :
--} Graphically, Number of zeroes is the number of times the graph of polynomial y = P(x) intersects the x - axis.
--} Graphically, Number of zeroes is the number of times the graph of polynomial x = P(y) intersects the y - axis.
--} Graph of polynomials :
(1) Linear polynomial : The graph of linear polynomials is always a straight line.
The standard form of linear polynomial is ax + b, a is not equal to zero.
(2) Quadratic polynomial : The graph of the quadratic polynomial is a parabola.
If a (Coefficient of x^2) is greater than zero or positive, then the graph is upward parabola.
If a (Coefficient of x^2) is less than zero or negative, then the graph is downward parabola.
The standard form of quadratic polynomial is ax^2 + bx + c, a is not equal to zero.
(3) Cubic polynomial : The graph of the cubic polynomial is a curve.
The standard form of cubic polynomial is ax^3 + bx^2 + cx + d, a is not equal to zero.
--} Example 1) Look at the graphs in the figure given below, Each is the graph of y = P(x), where P(x) is a polynomial. For each of the graphs, find the number of zeroes of P(x).
--} Exercise 2.1) Q. 1) The graphs of y = P(x) are given in the figure below, For some polynomial P(x). Find the number of zeroes of P(x) in each case.
--} Number of zeroes of y = P(x) is 2 from the figure given below. [March 2024]
--} The following figure shows the graph of polynomial y = P(x). In this case the number of zeroes of P(x) is 1. [June 2024]
--} As per given figure, y = P(x). The graph has 1 zero. [March 2026]
--} There are at most 2 zeroes for any cubic polynomial. [March 2026]
--} The graph of a polynomial intersects the x - axis at only one point, it cannot be a quadratic polynomial. [NCERT Exemplar]
--} If the graph of a polynomial intersects the x - axis at exactly two points, it need not be a quadratic polynomial. [NCERT Exemplar]
--} In the given figure y = P(x), the number of the zeroes of P(x) are ______. (2, 3, 4) [March 2022]
--} For the graph given below, x = P(y) has ________ zeroes. [June 2020]
--} The graph of P(x) = x^2 + 3x + 2 is a ________. (ray, line, parabola) [June 2022]
--} The graph of y = P(x) is given below. The number of zeroes of P(x) is _________. [June 2022]
(A) 1 (B) 2 (C) 3 (D) 0
--} For the given figure y = P(x), then the number of zeroes are _______. [March 2013, March 2023]
(A) 1 (B) 2 (C) 3 (D) 0
--} The graph of y = P(x) is given below, the number of zeroes of P(x) = _______. [March 2024]
(A) 1 (B) 2 (C) 3 (D) 0
--} The number of zeroes of y = P(x) from the graph is ________. [March 2017]
(A) 0 (B) 1 (C) 2 (D) 3
--} For the graph, in the figure y = P(x) has _______ zero(s). [March 2018]
(A) 3 (B) 1 (C) 2 (D) 4
--} The graph of P(x) = x^2 + 4x + 5 is drawn below, from this real zeroes is/are _______. [July 2018]
(A) 0 (B) 1 (C) 2 (D) 3
--} From the given figure, find the number of zeroes of y = P(x). [March 2018]
(A) 2 (B) 4 (C) 3 (D) 1
--} Which of the following is not a graph of a quadratic polynomial? [NCERT Exemplar]
--} The graph of linear polynomial P(x) = 5x + 3 is ________. [March 2019]
(A) Ray (B) Line (C) Parabola open upward (D) Parabola open polynomial
--} The zero of the standard form of linear polynomial in one variable is _______. [March 2019]
(A) a/b (B) b/a (C) -a/b (D) -b/a
--} Find the number of zeroes of y = P(x) from the figure given below. [March 2022]
--} What will be the graph of the equation 6x - 2x^2 + 7? [March 2020]