If \(p(x)=x^2-bx\), at which points does its graph intersect the x-axis?
Answer and explanation
Correct answer: \((0,0)\) and \((b,0)\)
Factor: \(p(x)=x^2-bx= x(x-b)\). x-intercepts occur where \(p(x)=0\), so \(x(x-b)=0\) gives \(x=0\) or \(x=b\). Thus the intercepts are \((0,0)\) and \((b,0)\). The closest distractor (B) is incorrect because \(p(-b)=(-b)^2-b(-b)=2b^2\), which is not zero for general \(b\ne0\). Option (D) is wrong since \((0,b)\) is on the y-axis, not the x-axis. Exam tip: set \(p(x)=0\) and factor out the common \(x\) to find x-intercepts quickly.
Frequently asked questions
What is the correct answer to this question?
\((0,0)\) and \((b,0)\)
Why is this the correct answer?
Factor: \(p(x)=x^2-bx= x(x-b)\). x-intercepts occur where \(p(x)=0\), so \(x(x-b)=0\) gives \(x=0\) or \(x=b\). Thus the intercepts are \((0,0)\) and \((b,0)\). The closest distractor (B) is incorrect because \(p(-b)=(-b)^2-b(-b)=2b^2\), which is not zero for general \(b\ne0\). Option (D) is wrong since \((0,b)\) is on the y-axis, not the x-axis. Exam tip: set \(p(x)=0\) and factor out the common \(x\) to find x-intercepts 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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