If a graph touches the x-axis at (9, 0) and crosses it at (-5, 0), what is the product of the zeroes?
Answer and explanation
Correct answer: -45
The x-values where the graph touches or crosses the x-axis are the zeroes. Here the zeroes are 9 and −5, so their product is 9×(−5)=−45. Note: touching usually means an even multiplicity and crossing means an odd multiplicity, but the numerical root values remain 9 and −5; unless the question asks for product counting multiplicities explicitly, use these root values. Option B (45) is the closest distractor but has the wrong sign. Exam tip: remember touch → even multiplicity, cross → odd multiplicity; for product-of-roots questions, multiply the root values given by the graph.
Frequently asked questions
What is the correct answer to this question?
-45
Why is this the correct answer?
The x-values where the graph touches or crosses the x-axis are the zeroes. Here the zeroes are 9 and −5, so their product is 9×(−5)=−45. Note: touching usually means an even multiplicity and crossing means an odd multiplicity, but the numerical root values remain 9 and −5; unless the question asks for product counting multiplicities explicitly, use these root values. Option B (45) is the closest distractor but has the wrong sign. Exam tip: remember touch → even multiplicity, cross → odd multiplicity; for product-of-roots questions, multiply the root values given by the graph.
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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