Which graph will give exactly two distinct real zeroes?
Answer and explanation
Correct answer: One that cuts the x-axis at two distinct points
The governing concept is the graphical interpretation of zeroes. A real zero is an x-value for which the function value is zero, so it is represented by a point where the graph meets the x-axis. If the graph cuts the x-axis at two different points, the two points have different x-coordinates and therefore give exactly two distinct real zeroes. Hence option A is correct. A graph staying above the x-axis has no real zero, while a graph touching the x-axis at only one point has one distinct real zero, often a repeated root for a quadratic. Intersections with the y-axis do not determine zeroes; they show the value p(0), and an ordinary function can meet the y-axis at only one point.
Frequently asked questions
What is the correct answer to this question?
One that cuts the x-axis at two distinct points
Why is this the correct answer?
The governing concept is the graphical interpretation of zeroes. A real zero is an x-value for which the function value is zero, so it is represented by a point where the graph meets the x-axis. If the graph cuts the x-axis at two different points, the two points have different x-coordinates and therefore give exactly two distinct real zeroes. Hence option A is correct. A graph staying above the x-axis has no real zero, while a graph touching the x-axis at only one point has one distinct real zero, often a repeated root for a quadratic. Intersections with the y-axis do not determine zeroes; they show the value p(0), and an ordinary function can meet the y-axis at only one point.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Geometrical meaning of the zeroes of a polynomial..
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