If p(x)=x^3-2x^2-5x+6, which of the following is not a zero?
Answer and explanation
Correct answer: 2
A number r is a zero of a polynomial p(x) exactly when p(r) = 0. Test each proposed value directly. p(1) = 1 − 2 − 5 + 6 = 0, so 1 is a zero. p(2) = 8 − 8 − 10 + 6 = −4, which is not zero; therefore 2 is not a zero. Also, p(3) = 27 − 18 − 15 + 6 = 0 and p(−2) = −8 − 8 + 10 + 6 = 0, so 3 and −2 are zeroes. The factorisation p(x) = (x − 1)(x − 3)(x + 2) confirms these results. Hence option B is uniquely correct. A nonzero substituted value, such as −4, is sufficient to disqualify a candidate as a zero.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
A number r is a zero of a polynomial p(x) exactly when p(r) = 0. Test each proposed value directly. p(1) = 1 − 2 − 5 + 6 = 0, so 1 is a zero. p(2) = 8 − 8 − 10 + 6 = −4, which is not zero; therefore 2 is not a zero. Also, p(3) = 27 − 18 − 15 + 6 = 0 and p(−2) = −8 − 8 + 10 + 6 = 0, so 3 and −2 are zeroes. The factorisation p(x) = (x − 1)(x − 3)(x + 2) confirms these results. Hence option B is uniquely correct. A nonzero substituted value, such as −4, is sufficient to disqualify a candidate as a zero.
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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