What are the zeroes of the polynomial \(x^3-6x^2+11x-6\)?
Answer and explanation
Correct answer: (1, 2, 3)
Factoring the polynomial gives \(x^3-6x^2+11x-6=(x-1)(x-2)(x-3)\). Setting each factor equal to zero gives \(x=1,2,3\), so option A is correct. The values in option C do not satisfy the required sum and product relationships for this cubic polynomial. Exam tip: For likely integer zeroes, substitute each candidate directly into the polynomial to verify it.
Frequently asked questions
What is the correct answer to this question?
(1, 2, 3)
Why is this the correct answer?
Factoring the polynomial gives \(x^3-6x^2+11x-6=(x-1)(x-2)(x-3)\). Setting each factor equal to zero gives \(x=1,2,3\), so option A is correct. The values in option C do not satisfy the required sum and product relationships for this cubic polynomial. Exam tip: For likely integer zeroes, substitute each candidate directly into the polynomial to verify it.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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