If \(p(x)=(x+7)(x-1)\), at which points will its graph intersect the x-axis?
Answer and explanation
Correct answer: \((-7,0)\) and \((1,0)\)
Intersection with the x-axis means \(p(x)=0\). Setting each factor to zero gives \(x+7=0\Rightarrow x=-7\) and \(x-1=0\Rightarrow x=1\). Thus the x-intercepts are \((-7,0)\) and \((1,0)\). Closest distractor: option A has the signs reversed (a common sign error); option B lists y-axis points, not x-axis intercepts. Exam tip: set each factor to zero and verify by substituting into \(p(x)\).
Frequently asked questions
What is the correct answer to this question?
\((-7,0)\) and \((1,0)\)
Why is this the correct answer?
Intersection with the x-axis means \(p(x)=0\). Setting each factor to zero gives \(x+7=0\Rightarrow x=-7\) and \(x-1=0\Rightarrow x=1\). Thus the x-intercepts are \((-7,0)\) and \((1,0)\). Closest distractor: option A has the signs reversed (a common sign error); option B lists y-axis points, not x-axis intercepts. Exam tip: set each factor to zero and verify by substituting into \(p(x)\).
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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