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
What does a zero of a polynomial (p(x)) represent geometrically?EasyLevel 22If the graph of a polynomial cuts the x-axis at x = 3, what is its zero?EasyLevel 22If a graph cuts the (x)-axis at ((-2,0)) and ((4,0)), what are the zeroes of the polynomial?EasyLevel 22If the graph of a linear polynomial cuts the (x)-axis only once, how many zeroes will it have?EasyLevel 22From which point can the zero of a polynomial be directly found?EasyLevel 22If the graph of a polynomial neither cuts nor touches the (x)-axis, how many real zeroes does it have?EasyLevel 22If a parabola cuts the (x)-axis at two distinct points, how many zeroes does the quadratic polynomial have?EasyLevel 22If a parabola only touches the (x)-axis and does not cut it, how many real zeroes does the quadratic polynomial have?EasyLevel 22If a parabola lies completely above the (x)-axis, how many real zeroes does the quadratic polynomial have?EasyLevel 22Which points on the graph indicate the zeros (roots) of a polynomial \\(p(x)\\)?EasyLevel 22If the graph of a polynomial crosses the x-axis at (0,0), what is one zero of the polynomial?EasyLevel 22If a graph cuts the x-axis at x = -5, which of the following statements is correct?EasyLevel 22If the points where a graph meets the (x)-axis are ((1,0)), ((2,0)), and ((5,0)), how many zeroes are there?EasyLevel 22What does the graph of a non-zero constant polynomial like (p(x)=5) show about its zeroes?EasyLevel 22If the graph of \(p(x)=x-4\) intersects the x-axis, what is the zero (root) of this polynomial?EasyLevel 22If the graph of the polynomial \(p(x)=x+2\) cuts the x-axis, what is its zero?EasyLevel 22What does the point (3, 0) on the graph of a polynomial represent?EasyLevel 22If the graph contains the point \((0,4)\), does that mean \(0\) is a zero of the function?EasyLevel 22If a polynomial graph has two intersections with the (x)-axis, how many real zeroes does it have?EasyLevel 22In which situation will (x=2) be called a zero of polynomial (p(x))?EasyLevel 22