Mathematics
Geometrical meaning of the zeroes of a polynomial.
बहुपद के शून्यकों का ज्यामितीय अर्थ
In this Class 10 Mathematics topic from Polynomials, students understand the geometrical meaning of a polynomial’s zeroes by connecting algebraic expressions with their graphs. A zero is represented by the x-coordinate where the graph meets or touches the x-axis. Students learn how the number of points of intersection indicates the number of real zeroes, and interpret graphs of linear, quadratic, and other polynomial functions to relate their shapes and x-intercepts to solutions of p(x) = 0.
Practice questions
If the zeros of a polynomial's graph are -6, 2 and 9, what is the correct set of x-axis intersection points?HardLevel 24If (p(x)=(x+5)(x-3)(x-9)), what will be the sign of (p(x)) for (3<x<9)?HardLevel 24If (p(x)=x^2-9x+k) has one zero (4), what will be the other zero and intersection points?HardLevel 24If a graph cuts the (x)-axis at (x=-8) and (x=8), which statement is most correct?HardLevel 24If \(p(x)=16x^2-9\), what are the x-axis intersections of the graph?HardLevel 24If the points meeting the (x)-axis are written as ((-5,0)), ((-5,0)), ((4,0)), how many distinct real zeroes are there?HardLevel 24If the graph of p(x) = x^2 + px + q cuts the x-axis at (-6, 0) and (2, 0), what will p and q be?HardLevel 24If a parabola cuts the (x)-axis at two points and cuts the (y)-axis at ((0,18)), what is the number of real zeroes?HardLevel 24If (p(x)=x^4-81), what are the real (x)-axis intersections?HardLevel 24If a polynomial cuts the (x)-axis at six distinct points, what is the minimum possible degree?HardLevel 24If (p(x)=x^2-2x+10), what is the graphical meaning of (p(x)=0)?HardLevel 24If (p(x)=x^3-8x^2+15x), what is the set of zeroes of the graph?HardLevel 24If a graph cuts the (x)-axis at ((6,0)) and ((18,0)), what is the position of (x=12) between them?HardLevel 24If p(x) = 4x^2 - 24x + 36, how will the graph meet the x-axis?MediumLevel 24If (p(x)=-(x-7)(x+9)), on which side of the (x)-axis will the graph lie for (x<-9)?HardLevel 24If a graph touches the x-axis at (7,0) and crosses it at (-4,0), what is the sum of the zeroes?HardLevel 24If the x-intercepts of a graph are (0,0) and (d,0) with \(d\neq0\), what is the product of the zeros?HardLevel 24If p(x) = x² − 15x + 56, what is the distance between the zeroes of the graph?MediumLevel 23If a parabola has zeroes (-4) and (10) and opens downward, where will the graph be outside the zeroes?HardLevel 24If (p(x)=x^8+1), what is the number of real zeroes of its graph?HardLevel 24