Chapter - 3 Polynomials | Class 10 | Complete Exercise - 3.2 Detailed Solution | Gyan Sagar Class 10

Ch-3 Polynomials Ex - 3.2 1. The graphs of y = p(x) are given in the figures below, for some polynomials p(x). In each case, find the number of zeroes of p(x). 2. Find the zeroes of the given polynomials. (i) p(x) = 3x (ii) p(x) = x² + 5x + 6 (iii) p(x) = (x+2) (x+3) (iv) p(x) = x⁴ – 16 3. Draw the graphs of the given polynomial and find the zeroes. Justify the answers. (i) p(x) = x² – x – 12 Steps: 1) Locate the points on a graph sheet, draw the graph. 2) we get graph shaped as a parabola. 3) The graph intersects at 2 points on x-axis. 4) In the graph, the parabola intersects x-axis at (-3,0) and (4,0). 5) So, the zeros of the quadratic equation are -3, 4. (ii) p(x) = x² – 6x + 9 Steps: 1) Locate the points on a graph sheet, draw the graph. 2) We get graph shaped as a parabola. 3) The graph touches 1 points on x-axis. 4) In the graph, the parabola intersects x-axis at (3,0). 5) So, the zero of the quadratic equation is 3. (iii) p(x) = x² – 4x + 5 Steps: 1) Locate the points on a graph sheet, draw the graph. 2) We get graph shaped as a parabola. 3) The Parabola does not intersect x-axis as p(x) has no real zeros. (iv) p(x) = x² + 3x – 4 Steps: 1) Locate the points on a graph sheet, draw the graph. 2) we get graph shaped as a parabola. 3) The graph intersects at 2 points on x-axis. 4) In the graph, the parabola intersects x-axis at (-1,0) and (4,0). 5) So, the zeros of the quadratic equation are -1, 4. (v) p(x) = x² – 1 Steps: 1) Locate the points on a graph sheet, draw the graph. 2) we get graph shaped as a parabola. 3) The graph intersects at 2 points on x-axis. 4) In the graph, the parabola intersects x-axis at (-1,0) and (1,0). 5) So, the zeros of the quadratic equation are -1, 1. 📌 Chapter - 3, Polynomials YouTube playlist - https://tinyurl.com/46jrh8zs 📌 Chapter - 3, Ex-3.1 YouTube playlist - https://tinyurl.com/yh84u7xp 📌 Chapter - 3, Ex-3.2 YouTube playlist - https://tinyurl.com/yh38nz96 📌 Chapter - 3, Ex-3.3 YouTube playlist - https://tinyurl.com/mryphnbj 📌 Chapter - 3, Ex-3.4 YouTube playlist - https://tinyurl.com/ywz2wha4 Hope you understand it and enjoy it, Thank you.