If a parabola touches the x-axis at the point (2,0) and opens upward, how many zeros (real roots) does it have?
Answer and explanation
Correct answer: One
Touching the x-axis means the parabola's vertex lies on the axis and the quadratic has a repeated root — one distinct real zero (a double root). In terms of discriminant, this corresponds to \\(\Delta=0\\). So there is exactly one real zero: x=2. Why other options are wrong: 'Two' would require the parabola to intersect the axis at two distinct points; 'None' applies when the parabola does not meet the axis at all; 'Infinite' is impossible for a polynomial of finite degree. Exam tip: for a double root of a quadratic check that \\(\Delta=0\\).
Frequently asked questions
What is the correct answer to this question?
One
Why is this the correct answer?
Touching the x-axis means the parabola's vertex lies on the axis and the quadratic has a repeated root — one distinct real zero (a double root). In terms of discriminant, this corresponds to \\(\Delta=0\\). So there is exactly one real zero: x=2. Why other options are wrong: 'Two' would require the parabola to intersect the axis at two distinct points; 'None' applies when the parabola does not meet the axis at all; 'Infinite' is impossible for a polynomial of finite degree. Exam tip: for a double root of a quadratic check that \\(\Delta=0\\).
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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