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 \(p(x)=4\), how is its graph related to the x-axis?EasyLevel 23If \(p(x)=x\), what is the zero (root) of the polynomial?EasyLevel 23If the zeroes of a graph are (-1), (3), and (8), at which points will it cut the (x)-axis?EasyLevel 23If a parabola has two real zeroes, how will it meet the (x)-axis?EasyLevel 23If a parabola has exactly one real zero, how will its graph meet the (x)-axis?EasyLevel 23If a graph cuts the (x)-axis at ((2,0)) and touches it at ((5,0)), how many distinct real zeroes are there?EasyLevel 23If the graph of a polynomial touches the x-axis at \,\((r,0)\\), what can be said about \,\(r\\)?EasyLevel 23If \(p(12)=0\), how will \(12\) appear on the graph?EasyLevel 23Which point on the graph shows that \,(x=11)\, is a zero of the polynomial?EasyLevel 23Which point on the graph indicates that x = -2 is a zero of the polynomial?EasyLevel 23If the graph of \(p(x)\) passes through the origin \((0,0)\), which x-value is a zero of the polynomial?EasyLevel 23If the points where a polynomial graph meets the (x)-axis are ((-9,0)), ((-1,0)), and ((3,0)), how many real zeroes are there?EasyLevel 23A graph contains the point (4, 2). Is \(x=4\) a zero of the polynomial represented by the graph?EasyLevel 23If a graph cuts the x-axis at (m, 0) and (n, 0), where m ≠ n, how many distinct real zeroes does it have?EasyLevel 23Which axis should be observed to see the zeroes on a graph?EasyLevel 23If the graph of a polynomial crosses the x-axis at the point \((7,0)\), what is the value of \(p(7)\)?EasyLevel 23If \(p(-4)=0\), at which point does the graph meet the x-axis?EasyLevel 23If a polynomial graph touches or cuts the (x)-axis exactly two times, how many real zeroes will it have?EasyLevel 23If a polynomial has no real zero, what will its graph do with the (x)-axis?EasyLevel 23If the graph of (p(x)) cuts the (x)-axis at ((u,0)), ((v,0)), and ((w,0)), what are the zeroes?EasyLevel 23