If a parabola only touches the x-axis, how many distinct real zeroes does the polynomial have?
Answer and explanation
Correct answer: One
A zero of a polynomial is represented by a point where its graph meets the x-axis. When a parabola only touches the x-axis, it meets the axis at exactly one point, so it has one distinct real zero. Algebraically, this corresponds to a repeated real root and the quadratic has discriminant zero. Thus the root may occur twice in factor form, but the number of distinct real zeroes is one, not two.
Frequently asked questions
What is the correct answer to this question?
One
Why is this the correct answer?
A zero of a polynomial is represented by a point where its graph meets the x-axis. When a parabola only touches the x-axis, it meets the axis at exactly one point, so it has one distinct real zero. Algebraically, this corresponds to a repeated real root and the quadratic has discriminant zero. Thus the root may occur twice in factor form, but the number of distinct real zeroes is one, not two.
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..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
