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
The x-axis intersections of a parabola are (r, 0) and (s, 0). What is the average of its zeroes?MediumLevel 22If the graph of a polynomial cuts the x-axis at the points (-4,0) and (4,0), which statement about the zeroes is correct?MediumLevel 22If the graph of a polynomial intersects the x-axis at the points (0,0), (2,0) and (5,0), which statement is correct?MediumLevel 22What is the zero of the line \(y=-3x-12\)?MediumLevel 22If (p(x)=x(x-5)), at which (x)-values will the graph cut the (x)-axis?MediumLevel 22For a polynomial, p(1) = 0, p(2) = 0, and p(3) = 0. If these are three distinct zeroes, at how many distinct points will the graph meet the x-axis?EasyLevel 22If (p(-2)=0) and (p(2)=0), how are the zeroes positioned with respect to the (y)-axis?MediumLevel 22A graph crosses the x-axis at x = 1 and x = 4. If p(2) > 0, why is x = 2 not a zero?MediumLevel 22If the graph of a cubic polynomial cuts the (x)-axis only once, what is the number of real zeroes?MediumLevel 22If a quadratic graph stays below the (x)-axis and does not touch it, which statement is correct?MediumLevel 22If x = 7 is a zero of a polynomial, which point must lie on its graph?MediumLevel 22A graph has x-axis intercepts (a,0), (b,0), (c,0). Which statement is correct?MediumLevel 22If (p(x)=2(x-3)^2), how will the graph meet the (x)-axis?MediumLevel 22If p(x) = -x^2 + 25, what are the real zeros of its graph?MediumLevel 22If (-2, 0) and (6, 0) are the zero points of a graph, what is the distance between them on the x-axis?MediumLevel 22If (p(0)=0) and (p(5)=0), which statement about the graph is correct?MediumLevel 22If the graph of p(x) crosses the x-axis at (2, 0) and touches it at (-1, 0), how many distinct real zeros does p(x) have?MediumLevel 22A polynomial graph does not cut the (x)-axis, but (p(1)=4) and (p(3)=9). What is the correct conclusion?MediumLevel 22If a graph cuts the (x)-axis at ((-3,0)), ((2,0)), ((8,0)), which is the smallest zero?MediumLevel 22In a polynomial graph, there is a touch with the (x)-axis at (x=4) and a crossing at (x=-6). Which statement is correct?MediumLevel 22