If a parabola remains entirely above the x-axis and never touches it, how many real zeroes does it have?
Answer and explanation
Correct answer: Zero
A real zero of a polynomial is an x-value for which p(x) = 0; geometrically, it is an x-coordinate where the graph meets the x-axis. If the entire parabola lies above the x-axis and never touches or crosses it, no point on the graph has y-coordinate 0. Therefore the polynomial has zero real zeroes, so option A is correct. A parabola tangent to the x-axis would have one repeated real zero, and a parabola crossing it at two points would have two distinct real zeroes. It cannot have infinitely many zeroes because a nonzero quadratic has at most two real zeroes.
Frequently asked questions
What is the correct answer to this question?
Zero
Why is this the correct answer?
A real zero of a polynomial is an x-value for which p(x) = 0; geometrically, it is an x-coordinate where the graph meets the x-axis. If the entire parabola lies above the x-axis and never touches or crosses it, no point on the graph has y-coordinate 0. Therefore the polynomial has zero real zeroes, so option A is correct. A parabola tangent to the x-axis would have one repeated real zero, and a parabola crossing it at two points would have two distinct real zeroes. It cannot have infinitely many zeroes because a nonzero quadratic has at most two real zeroes.
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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