If \(p(x)=36x^2-49\), what are the x-axis intersections of its graph?
Answer and explanation
Correct answer: \(\left(\frac{7}{6},0\right),\ \left(-\frac{7}{6},0\right)\)
To find x-axis intersections, set \(p(x)=0\). Since \(36x^2-49=(6x-7)(6x+7)\), the equation \((6x-7)(6x+7)=0\) gives \(x=\frac{7}{6}\) or \(x=-\frac{7}{6}\). Therefore, the intercepts are \(\left(\frac{7}{6},0\right)\) and \(\left(-\frac{7}{6},0\right)\). Option C incorrectly uses the reciprocal \(\frac{6}{7}\). Exam tip: factor a difference of squares \(a^2-b^2\) as \((a-b)(a+b)\) before solving.
Frequently asked questions
What is the correct answer to this question?
\(\left(\frac{7}{6},0\right),\ \left(-\frac{7}{6},0\right)\)
Why is this the correct answer?
To find x-axis intersections, set \(p(x)=0\). Since \(36x^2-49=(6x-7)(6x+7)\), the equation \((6x-7)(6x+7)=0\) gives \(x=\frac{7}{6}\) or \(x=-\frac{7}{6}\). Therefore, the intercepts are \(\left(\frac{7}{6},0\right)\) and \(\left(-\frac{7}{6},0\right)\). Option C incorrectly uses the reciprocal \(\frac{6}{7}\). Exam tip: factor a difference of squares \(a^2-b^2\) as \((a-b)(a+b)\) before solving.
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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