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 point on the graph represents a zero (root) of the polynomial \(p(x)\)?EasyLevel 24If the graph of a linear polynomial cuts the (x)-axis once then how many zeroes does it have?EasyLevel 24If the graph of a quadratic polynomial cuts the (x)-axis at two distinct points then what is the number of real zeroes?EasyLevel 24If a parabola only touches the x-axis, how many distinct real zeroes does the polynomial have?EasyLevel 24If the graph of a quadratic polynomial does not meet the (x)-axis anywhere then how many real zeroes does it have?EasyLevel 24If the graph of a polynomial passes through the point \((4,0)\), which statement is correct?EasyLevel 24If the graph of a polynomial passes through the origin (0,0), which zero must the polynomial have?EasyLevel 24If the graph cuts the x-axis at -2, what is the zero of the polynomial?EasyLevel 24A graph cuts the x-axis at x = -3 and x = 5. What are its real zeroes?EasyLevel 24If the graph of a polynomial is parallel to the x-axis and does not intersect it, how many zeroes does the polynomial have?EasyLevel 24At which point will the graph of \(p(x)=x-7\) intersect the x-axis?EasyLevel 24What is the x-axis intersection point of the graph of \(p(x)=x+4\)?EasyLevel 24At which x-value does the zero (root) of the polynomial \(p(x)=2x-6\) lie on its graph?EasyLevel 24If the graph cuts the x-axis at (6, 0) then what is the value of p(6)?EasyLevel 24If \(p(-1)=0\), then which statement about the graph of the polynomial is correct?EasyLevel 24The graph of a polynomial intersects the y-axis at the point (0, 5). Is x = 0 a zero of the polynomial?EasyLevel 24The graph only touches the x-axis at (2, 0). Which is the zero?EasyLevel 24A parabola opens upward and has vertex ((0,3)). If it does not cut the (x)-axis then how many real zeroes are there?EasyLevel 24If a quadratic polynomial has real zeroes 1 and 4, at which points will its graph cut the x-axis?EasyLevel 24If the graph crosses the x-axis at (-5, 0) and (2, 0), what is the sum of the zeroes?EasyLevel 24