If \(p(x)=4x^2-25\), what are the x-axis intercepts of its graph?
Answer and explanation
Correct answer: \(\left(\frac{5}{2},0\right)\) and \(\left(-\frac{5}{2},0\right)\)
x-intercepts occur where \(p(x)=0\). From \(4x^2-25=0\) we get \(4x^2=25\), so \(x^2=\tfrac{25}{4}\) and hence \(x=\pm\tfrac{5}{2}\). Therefore the intercepts are \(\left(\tfrac{5}{2},0\right)\) and \(\left(-\tfrac{5}{2},0\right)\). Alternatively factor \(4x^2-25=(2x-5)(2x+5)\) to read off the roots. The closest distractor (B) reflects a common slip of using 5 instead of \(\tfrac{5}{2}\). Exam tip: treat \(4x^2\) as \((2x)^2\) or take square roots carefully to avoid fraction errors.
Frequently asked questions
What is the correct answer to this question?
\(\left(\frac{5}{2},0\right)\) and \(\left(-\frac{5}{2},0\right)\)
Why is this the correct answer?
x-intercepts occur where \(p(x)=0\). From \(4x^2-25=0\) we get \(4x^2=25\), so \(x^2=\tfrac{25}{4}\) and hence \(x=\pm\tfrac{5}{2}\). Therefore the intercepts are \(\left(\tfrac{5}{2},0\right)\) and \(\left(-\tfrac{5}{2},0\right)\). Alternatively factor \(4x^2-25=(2x-5)(2x+5)\) to read off the roots. The closest distractor (B) reflects a common slip of using 5 instead of \(\tfrac{5}{2}\). Exam tip: treat \(4x^2\) as \((2x)^2\) or take square roots carefully to avoid fraction errors.
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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