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 of the polynomial \(p(x)\) intersects the x-axis at the point \((a,0)\), what is the value of \(p(a)\)?EasyLevel 23If \(p(0)=4\), is \(0\) a zero (root) of the polynomial \(p(x)\)?EasyLevel 23At what x-value does the line \(y=3x-12\) intersect the x-axis?EasyLevel 23What is the zero of the line \(y = x - 8\)?EasyLevel 23What is the zero (x-intercept) of the line \(y = x + 9\)?EasyLevel 23If \(p(x)=2x+6\), at which x-value will its graph cut the x-axis?EasyLevel 23If the graph of a polynomial cuts the x-axis at the point (10, 0), which of the following statements is correct?EasyLevel 23If the graph of a polynomial passes through the point \((0,7)\), does this prove that \(x=0\) is a zero (root) of the polynomial?EasyLevel 23If the graph of a polynomial intersects the x-axis at the points (-7,0), (0,0) and (4,0), what are the zeroes of the polynomial?EasyLevel 23Why does the graph of the non-zero constant polynomial (p(x)=-3) not cut the (x)-axis?EasyLevel 23If (p(c)=0), what is (c) called?EasyLevel 23If the graph shows the point (-8, 0), for which value of x does the polynomial equal zero?EasyLevel 23If a graph intersects the \\(x\\)-axis at \\(x=2\\) and \\(x=9\\), what are the values of \\(p(2)\\) and \\(p(9)\\)?EasyLevel 23If a parabola has its vertex at (-2, 0) and it touches the x-axis at that point, what is its zero?EasyLevel 23Which graph will give zeroes (1) and (-6)?EasyLevel 23If a graph only touches the (x)-axis, will that point give a zero?EasyLevel 23If a graph lies completely below the (x)-axis and does not touch it, how many real zeroes does it have?EasyLevel 23If \(p(5)\neq 0\), what can be said about \(5\)?EasyLevel 23If \(p(-10)=0\), which corresponding point will lie on the \(x\)-axis?EasyLevel 23What does the number of distinct meeting points with the (x)-axis tell in a polynomial graph?EasyLevel 23