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 p(x)=(x−2)(x+6)^3, what are the distinct zeroes?MediumLevel 23If the (x)-axis intersections of a parabola are ((-9,0)) and ((3,0)), what is the coordinate of the midpoint?HardLevel 23If a graph cuts the x-axis at x=-10, x=-4, and x=6, what is the range of the zeroes?MediumLevel 23If (p(x)=x^2-4x-21), what are the (x)-axis intersections of the graph?HardLevel 23If the graph of a polynomial function intersects the y-axis at the origin (0,0), which conclusion about its zeros is correct?HardLevel 23If (p(x)=x^2-12x+36), at which point will the graph touch the (x)-axis?HardLevel 23If the (x)-axis intersections of a graph are ((a,0)), ((b,0)), ((c,0)), what will be the product of the zeroes?HardLevel 23If (p(x)=x^2+4x+8), why will the graph not cut the (x)-axis?HardLevel 23If (p(x)=x(x-3)^2(x+5)), what will be the graph behavior at (x=3)?HardLevel 23If the zeroes of a parabola are (b-5) and (b+1), what will be its axis of symmetry?HardLevel 23If the zeros of a graph are -4, 1 and 8, what is the correct set of x-axis intersection points?HardLevel 23If (p(x)=(x+4)(x-2)(x-7)), what will be the sign of (p(x)) for (2<x<7)?HardLevel 23If (p(x)=x^2-7x+k) has one zero (3), what will be the other zero and intersection points?HardLevel 23If a graph cuts the (x)-axis at (x=-6) and (x=6), which statement is most correct?HardLevel 23If p(x)=9x^2-16, what are the x-axis intersections (x-intercepts) of its graph?HardLevel 23If the points meeting the x-axis are written as (2,0), (2,0), (9,0), how many distinct real zeroes are there?MediumLevel 23If the graph of p(x)=x^2+px+q cuts the x-axis at (-4,0) and (3,0), what will p and q be?MediumLevel 23If a parabola cuts the (x)-axis at two points and cuts the (y)-axis at ((0,-15)), what is the number of real zeroes?HardLevel 23If (p(x)=x^4-16), what are the real (x)-axis intersections?HardLevel 23If a polynomial cuts the (x)-axis at four distinct points, what is the minimum possible degree?HardLevel 23