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 \(p(-1)=0\), through which point will the graph pass?EasyLevel 22If \(p(6)=0\), at which point does the polynomial graph intersect the x-axis?EasyLevel 22If the graph of a quadratic polynomial cuts the (x)-axis at ((2,0)) and ((7,0)), what are the zeroes?EasyLevel 22If the vertex of a parabola lies on the (x)-axis at (x=4), what is the real zero?EasyLevel 22Which graph will give zeroes (-3) and (2)?EasyLevel 22If a polynomial graph cuts only the (y)-axis at ((0,3)) and does not cut the (x)-axis, how many real zeroes are there?EasyLevel 22In the graph of the polynomial p(x), where y = p(x), what is the value of y at a zero of the polynomial?EasyLevel 22If the line \(y=2x-6\) cuts the x-axis, what is the zero of the corresponding linear polynomial?EasyLevel 22If the graph of the line \(y = x + 7\) cuts the x-axis, what is the zero (x-intercept)?EasyLevel 22If the graph of a polynomial touches the x-axis only at the point (5,0), which of the following statements is correct?EasyLevel 22If the number of intersections of a polynomial graph with the (x)-axis is (4), how many real zeroes are there?EasyLevel 22If \(p(2)=5\), is 2 a zero of the polynomial \(p(x)\)?EasyLevel 22If p(a)=0, through which point must the graph pass?EasyLevel 22If a graph cuts the (x)-axis at (x=1), (x=3), and (x=6), what are the zeroes?EasyLevel 22If a parabola cuts the x-axis at (-1, 0) and (5, 0), how many real zeros does it have?EasyLevel 22If a parabola touches the x-axis at the point (2,0) and opens upward, how many zeros (real roots) does it have?EasyLevel 22In which case will a quadratic polynomial have two real zeroes?EasyLevel 22In which case will a quadratic polynomial have no real zero?EasyLevel 22What does the number of intersections with the (x)-axis tell in a polynomial graph?EasyLevel 22If the graph of a polynomial crosses the x-axis at (-4, 0), which value of x makes the polynomial zero?EasyLevel 22