If p(x) = x^3 - 2x^2 - 13x - 10, which of the following is a zero of p(x)?
Answer and explanation
Correct answer: -2
The governing concept is the zero test: a number r is a zero of p(x) exactly when p(r) = 0. Test the options by substitution. For r = -2, p(-2) = (-2)^3 - 2(-2)^2 - 13(-2) - 10 = -8 - 8 + 26 - 10 = 0. Therefore -2 is a zero and option D is correct. For comparison, p(5) = 125 - 50 - 65 - 10 = 0 as well, so 5 is also a zero. This means the question has two correct options, A and D, contrary to the supplied key. Indeed, the polynomial factors as (x - 5)(x + 2)(x + 1), confirming both 5 and -2 are zeros.
Frequently asked questions
What is the correct answer to this question?
-2
Why is this the correct answer?
The governing concept is the zero test: a number r is a zero of p(x) exactly when p(r) = 0. Test the options by substitution. For r = -2, p(-2) = (-2)^3 - 2(-2)^2 - 13(-2) - 10 = -8 - 8 + 26 - 10 = 0. Therefore -2 is a zero and option D is correct. For comparison, p(5) = 125 - 50 - 65 - 10 = 0 as well, so 5 is also a zero. This means the question has two correct options, A and D, contrary to the supplied key. Indeed, the polynomial factors as (x - 5)(x + 2)(x + 1), confirming both 5 and -2 are zeros.
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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