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 \(p(0)=0\), through which special point will the polynomial's graph pass?EasyLevel 22Which polynomial's graph will intersect the x-axis at x = 0?EasyLevel 22If the graph of a polynomial cuts the x-axis at \((a,0)\), what is the zero of the polynomial?EasyLevel 22By what name can the zeroes of a polynomial also be understood on a graph?EasyLevel 22If a polynomial graph cuts the (x)-axis once and touches it once, how many distinct real zeroes will it have?EasyLevel 22If the graph of a polynomial crosses the \\x-axis at \\( (8,0) \\), what is the value of \\(p(8)\\)?EasyLevel 22If \(p(-6)=0\), which point lies on the graph?EasyLevel 22If a graph has no common point with the (x)-axis, what is the conclusion about its zeroes?EasyLevel 22The graph of a polynomial touches the x-axis only at (-2, 0). What is the distinct real zero?EasyLevel 22If a graph cuts the x-axis at (r, 0) and (s, 0), where r ≠ s, what are the zeroes?EasyLevel 22Which quantity must be zero for a point on the graph of a polynomial to be called a zero (root) of the polynomial?EasyLevel 23If a graph cuts the (x)-axis at ((-4,0)) and ((1,0)), what are the zeroes?EasyLevel 23If the graph of a polynomial meets the x-axis at only one point, which is (6,0), what is the distinct real zero of the polynomial?EasyLevel 23If \(p(9)=0\), through which point will the graph pass?EasyLevel 23If \(p(-3)=0\), which value is a zero of the polynomial?EasyLevel 23Why does the intersection of a graph with the (y)-axis not directly give a zero?EasyLevel 23If a graph cuts the (x)-axis at three distinct points, how many real zeroes will it have?EasyLevel 23If a parabola has no common point with the (x)-axis, how many real zeroes does the quadratic polynomial have?EasyLevel 23If a parabola only touches the (x)-axis at ((3,0)), how many real zeroes does the quadratic polynomial have?EasyLevel 23If a parabola cuts the x-axis at the points (-5, 0) and (2, 0), what are its zeroes?EasyLevel 23