If \(p(x)=x^2-ax\), what are the x-axis intercepts (x-intercepts) of its graph?
Answer and explanation
Correct answer: \((0,0),\; (a,0)\)
Set \(p(x)=0\). Factor: \(p(x)=x^2-ax=x(x-a)\). Thus the roots are \(x=0\) and \(x=a\), so the x-intercepts are \((0,0)\) and \((a,0)\). The closest distractor \((0,0),(-a,0)\) is wrong because it flips the sign of the second root; sign errors are common when factoring or solving. Exam tip: always factor and set each factor equal to zero; intercepts have y-coordinate 0, so give points of the form \((\text{root},0)\).
Frequently asked questions
What is the correct answer to this question?
\((0,0),\; (a,0)\)
Why is this the correct answer?
Set \(p(x)=0\). Factor: \(p(x)=x^2-ax=x(x-a)\). Thus the roots are \(x=0\) and \(x=a\), so the x-intercepts are \((0,0)\) and \((a,0)\). The closest distractor \((0,0),(-a,0)\) is wrong because it flips the sign of the second root; sign errors are common when factoring or solving. Exam tip: always factor and set each factor equal to zero; intercepts have y-coordinate 0, so give points of the form \((\text{root},0)\).
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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