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(5) = 0 and p(−2) = 0, at which x-values will the graph cut the x-axis?EasyLevel 24A student looked at the point (0, 7) and called 7 a zero of a polynomial. What is the mistake in this reasoning?EasyLevel 24A parabola touches the (x)-axis only at ((2,0)). What is the number of distinct real zeroes?EasyLevel 24If a graph passes through the points \\((1,0)\\), \\((4,0)\\) and \\((0,6)\\), what are the zeroes?EasyLevel 24If the points cutting the (x)-axis are ((-7,0)) and ((-3,0)) then which is the greater zero?EasyLevel 24If the graph of \\(p(x)=x^2-9\\) is drawn, what are the x-axis intersections (x-intercepts)?EasyLevel 24How does the graph of \(p(x)=x^2\) meet the x-axis?EasyLevel 24If p(x) = (x-2)(x+5), at which points will its graph intersect the x-axis?EasyLevel 24What is the main use of counting x-axis intersections in a polynomial graph?EasyLevel 24If a polynomial graph has only one x-axis intersection at x = −8, which statement is correct?EasyLevel 24A polynomial graph cuts the x-axis at (−4, 0), (1, 0), and (6, 0). How many real zeroes does it have?MediumLevel 22If the parabola of a quadratic polynomial only touches the (x)-axis at ((3,0)), what is the number of distinct real zeroes?MediumLevel 22A graph stays entirely above the (x)-axis and never cuts it. How many real zeroes does that polynomial have?MediumLevel 22If \(p(a)=0\) and \(p(b)=0\), where \(a\neq b\), at which points will the graph of \(p(x)\) cut the x-axis?MediumLevel 22A polynomial graph passes through ((0,-5)), ((2,0)), ((5,0)) and ((7,3)). What are its zeroes?MediumLevel 22A student saw the y-axis intercept (0,8) and took 8 to be a zero (root) of the polynomial. What is the correct correction?MediumLevel 22What will be the x-axis intersections of the graph of p(x) = (x − 4)(x + 2)?MediumLevel 22Where will the line y = 2x − 10 cut the x-axis?MediumLevel 22If the x-axis intersections of a parabola are \\((-1,0)\\) and \\((4,0)\\), what is the sum of its zeroes?MediumLevel 22If a graph cuts the (x)-axis at ((-6,0)) and ((2,0)), what is the product of zeroes?MediumLevel 22