If a parabola only touches the (x)-axis at ((3,0)), how many real zeroes does the quadratic polynomial have?
Answer and explanation
Correct answer: One
The zeroes of a polynomial are the x-coordinates where its graph meets the x-axis. A graph that crosses the axis usually gives a zero with a sign change, while a graph that only touches the axis and turns back gives a repeated zero. Although the zero may be repeated algebraically, its distinct real value is counted as one real zero in this question.
The parabola touches the x-axis at the single point \((3,0)\). Thus the corresponding value of x is \(x=3\), and there is no second point of intersection. For example, a polynomial such as \((x-3)^2\) has the repeated root 3, but only one distinct real zero. Therefore option A, one, is correct.
Frequently asked questions
What is the correct answer to this question?
One
Why is this the correct answer?
The zeroes of a polynomial are the x-coordinates where its graph meets the x-axis. A graph that crosses the axis usually gives a zero with a sign change, while a graph that only touches the axis and turns back gives a repeated zero. Although the zero may be repeated algebraically, its distinct real value is counted as one real zero in this question.
The parabola touches the x-axis at the single point \((3,0)\). Thus the corresponding value of x is \(x=3\), and there is no second point of intersection. For example, a polynomial such as \((x-3)^2\) has the repeated root 3, but only one distinct real zero. Therefore option A, one, is correct.
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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