If the graph of a polynomial crosses the x-axis at \\(x=-3\\) and only touches it at \\(x=2\\), which statement is correct?
Answer and explanation
Correct answer: Both are real zeroes
If a polynomial's graph either crosses or merely touches the x-axis at a value of x, the polynomial equals zero at that x (\\(p(x)=0\\)). Therefore both x = -3 (crossing) and x = 2 (touching) are real zeroes. Geometrically, crossing usually indicates an odd multiplicity (often 1) and touching indicates an even multiplicity (\\(\ge2\\)), but both imply roots. The closest distractor B is wrong because 'touching' still means the polynomial vanishes there. Exam tip: check whether the graph crosses or touches the axis — that tells you the presence of a root and suggests whether its multiplicity is odd or even.
Frequently asked questions
What is the correct answer to this question?
Both are real zeroes
Why is this the correct answer?
If a polynomial's graph either crosses or merely touches the x-axis at a value of x, the polynomial equals zero at that x (\\(p(x)=0\\)). Therefore both x = -3 (crossing) and x = 2 (touching) are real zeroes. Geometrically, crossing usually indicates an odd multiplicity (often 1) and touching indicates an even multiplicity (\\(\ge2\\)), but both imply roots. The closest distractor B is wrong because 'touching' still means the polynomial vanishes there. Exam tip: check whether the graph crosses or touches the axis — that tells you the presence of a root and suggests whether its multiplicity is odd or even.
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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