If p(x) = 2(x-1)(x+4), what are the x-intercepts of its graph?
Answer and explanation
Correct answer: (1,0) and (-4,0)
The polynomial is given in factor form: p(x)=2(x-1)(x+4). x-intercepts occur where p(x)=0, so set each factor to zero: x-1=0 → x=1 and x+4=0 → x=-4. Hence the intercepts are (1,0) and (-4,0). The multiplicative constant 2 does not affect the roots. Closest distractor B flips the signs, C wrongly uses 2 instead of 1, and D lists y-intercepts. Exam tip: from factorised form read off roots directly and write intercepts as (root,0).
Frequently asked questions
What is the correct answer to this question?
(1,0) and (-4,0)
Why is this the correct answer?
The polynomial is given in factor form: p(x)=2(x-1)(x+4). x-intercepts occur where p(x)=0, so set each factor to zero: x-1=0 → x=1 and x+4=0 → x=-4. Hence the intercepts are (1,0) and (-4,0). The multiplicative constant 2 does not affect the roots. Closest distractor B flips the signs, C wrongly uses 2 instead of 1, and D lists y-intercepts. Exam tip: from factorised form read off roots directly and write intercepts as (root,0).
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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