If \(p(x)=x^2-cx\), what are the x-axis intersections (x-intercepts) of its graph?
Answer and explanation
Correct answer: (0,0) and (c,0)
We have \(p(x)=x^2-cx\). Factor the expression: \(p(x)=x(x-c)\). Setting \(p(x)=0\) gives \(x=0\) or \(x=c\). Therefore the x-intercepts are \((0,0)\) and \((c,0)\). Why others are wrong: option B uses \(-c\) which is the wrong sign; option C omits the zero at \(x=0\); option D includes \((0,c)\), a point on the y-axis, not an x-intercept. Exam tip: set \(p(x)=0\) and factor out the common \(x\) to find zeros quickly.
Frequently asked questions
What is the correct answer to this question?
(0,0) and (c,0)
Why is this the correct answer?
We have \(p(x)=x^2-cx\). Factor the expression: \(p(x)=x(x-c)\). Setting \(p(x)=0\) gives \(x=0\) or \(x=c\). Therefore the x-intercepts are \((0,0)\) and \((c,0)\). Why others are wrong: option B uses \(-c\) which is the wrong sign; option C omits the zero at \(x=0\); option D includes \((0,c)\), a point on the y-axis, not an x-intercept. Exam tip: set \(p(x)=0\) and factor out the common \(x\) to find zeros quickly.
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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