If \(p(x)=x^2-2x\), at which \(x\)-values does its graph intersect the \(x\)-axis?
Answer and explanation
Correct answer: 0 and 2
Set \(p(x)=0\). Factorizing gives \(x^2-2x=x(x-2)\), so \(x(x-2)=0\) implies \(x=0\) or \(x=2\). Thus the graph meets the x-axis at \(x=0\) and \(x=2\). Closest distractor B is incorrect because \(p(1)=1-2=-1\), not zero. C and D are also wrong since the factorization shows two distinct zeros. Exam tip: factor out the common term first to find zeros quickly.
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What is the correct answer to this question?
0 and 2
Why is this the correct answer?
Set \(p(x)=0\). Factorizing gives \(x^2-2x=x(x-2)\), so \(x(x-2)=0\) implies \(x=0\) or \(x=2\). Thus the graph meets the x-axis at \(x=0\) and \(x=2\). Closest distractor B is incorrect because \(p(1)=1-2=-1\), not zero. C and D are also wrong since the factorization shows two distinct zeros. Exam tip: factor out the common term first 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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