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 graph cuts the x-axis at (−2, 0) and (3, 0), then what is the product of the zeroes?EasyLevel 24In the graph, the points (0,0) and (3,0) lie on the x-axis. What are the possible zeroes of the corresponding polynomial?EasyLevel 24The graph of a cubic polynomial cuts the x-axis at three distinct points. What is the number of real zeroes?EasyLevel 24For the zero polynomial \(p(x)=0\), what is every \(x\)-value called?EasyLevel 24What is the relation of the graph of the non-zero constant polynomial (p(x)=5) with the (x)-axis?EasyLevel 24What is the x-axis intersection point of the graph of p(x)=3x?EasyLevel 24If the line \(y = x + 2\) cuts the x-axis, what is the x-coordinate of the point of intersection?EasyLevel 24If the graph of the line \(y=5-x\) is given, what is its zero (the x-value where y = 0)?EasyLevel 24Only the point ((8,0)) is visible on the (x)-axis in the graph. What is the number of real zeroes of the polynomial?EasyLevel 24If the x-axis intersection of a polynomial graph is (a, 0), what is the zero?EasyLevel 24If \(p(2)=3\) then the point \((2,3)\) lies on the graph. Is 2 a zero (root) of \(p(x)\)?EasyLevel 24If \(p(-4)=0\), through which point must the graph of \(y=p(x)\) pass?EasyLevel 24Which of the following points geometrically represents a zero of a polynomial directly?EasyLevel 24The graph intersects the x-axis at (-1, 0) and (1, 0). What is the sum of the zeros?EasyLevel 24If a parabola cuts the (x)-axis at ((0,0)) and ((6,0)) then what is the product of zeroes?EasyLevel 24Which graph will give two real zeroes?EasyLevel 24In which situation will x = 3 be a zero of the polynomial?EasyLevel 24In which situation will (-6) be a zero of the polynomial?EasyLevel 24If no point of a polynomial graph lies on the x-axis, which statement is correct?EasyLevel 24If the graph of a polynomial cuts the \\(x\\)-axis at \\(x=10\\), which of the following statements is true?EasyLevel 24