If \(p(x)=-(x-1)(x+4)\), at which real zeros (x-intercepts) does its graph cross the x-axis?
Answer and explanation
Correct answer: (1) and (-4)
Core idea: zeros occur when the product equals zero, so at least one factor must be zero. From \(-(x-1)(x+4)=0\) the leading minus sign does not change the roots; it only flips the overall sign. Set each factor to zero: \(x-1=0\) gives \(x=1\), and \(x+4=0\) gives \(x=-4\). Choice B is wrong because the signs are reversed; C and D are not obtained from the given factors. Exam tip: to find x-intercepts of a factored polynomial, set each factor equal to zero and solve.
Frequently asked questions
What is the correct answer to this question?
(1) and (-4)
Why is this the correct answer?
Core idea: zeros occur when the product equals zero, so at least one factor must be zero. From \(-(x-1)(x+4)=0\) the leading minus sign does not change the roots; it only flips the overall sign. Set each factor to zero: \(x-1=0\) gives \(x=1\), and \(x+4=0\) gives \(x=-4\). Choice B is wrong because the signs are reversed; C and D are not obtained from the given factors. Exam tip: to find x-intercepts of a factored polynomial, set each factor equal to zero and solve.
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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