If \(p(x)=-(x-3)(x+1)\), what are the zeros of its graph?
Answer and explanation
Correct answer: (3) and (-1)
Zeros are the x-values for which \(p(x)=0\). A multiplicative constant (the leading '-' here) does not change the roots. Set each factor equal to zero: \(x-3=0\) gives \(x=3\), and \(x+1=0\) gives \(x=-1\). Thus the zeros are 3 and -1. Why distractors fail: option D mistakenly uses +1 instead of -1; option B flips signs of both roots. Exam tip: Factor the polynomial and set each linear factor to zero; ignore overall constant factors when finding zeros.
Frequently asked questions
What is the correct answer to this question?
(3) and (-1)
Why is this the correct answer?
Zeros are the x-values for which \(p(x)=0\). A multiplicative constant (the leading '-' here) does not change the roots. Set each factor equal to zero: \(x-3=0\) gives \(x=3\), and \(x+1=0\) gives \(x=-1\). Thus the zeros are 3 and -1. Why distractors fail: option D mistakenly uses +1 instead of -1; option B flips signs of both roots. Exam tip: Factor the polynomial and set each linear factor to zero; ignore overall constant factors when finding zeros.
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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