How does the graph of \(p(x)=x^2\) meet the x-axis?
Answer and explanation
Correct answer: It touches the x-axis at the origin \(x=0\)
Solve \(x^2=0\) to find zeros: the only root is \(x=0\), with multiplicity 2. A repeated root of even multiplicity means the parabola touches (is tangent to) the x-axis at that point and does not cross it. Option B is incorrect because two distinct real roots would be required to cut the axis at two points (discriminant > 0), which is not the case here. Option D is wrong since \(x=1\) is not a root. Exam tip: check factorization or discriminant and note root multiplicities to determine whether the graph crosses or merely touches the x-axis.
Frequently asked questions
What is the correct answer to this question?
It touches the x-axis at the origin \(x=0\)
Why is this the correct answer?
Solve \(x^2=0\) to find zeros: the only root is \(x=0\), with multiplicity 2. A repeated root of even multiplicity means the parabola touches (is tangent to) the x-axis at that point and does not cross it. Option B is incorrect because two distinct real roots would be required to cut the axis at two points (discriminant > 0), which is not the case here. Option D is wrong since \(x=1\) is not a root. Exam tip: check factorization or discriminant and note root multiplicities to determine whether the graph crosses or merely touches the x-axis.
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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