If \(p(x)=x^2-49\), at which points does its graph intersect the x-axis?
Answer and explanation
Correct answer: (7, 0) and (-7, 0)
x-intercepts occur where the polynomial equals zero. Factorizing gives \(p(x)=x^2-49=(x-7)(x+7)\). Setting \(p(x)=0\) yields \(x=\pm7\), so the graph meets the x-axis at \((7,0)\) and \((-7,0)\). Option C is a common confusion: \((0,7)\) and \((0,-7)\) are y-intercepts, not x-intercepts. Option B would require zeros at \(x=\pm49\) which correspond to \(x^2-2401\), not our polynomial. Exam tip: to find x-intercepts set \(p(x)=0\) and factor; recognize difference of squares quickly.
Frequently asked questions
What is the correct answer to this question?
(7, 0) and (-7, 0)
Why is this the correct answer?
x-intercepts occur where the polynomial equals zero. Factorizing gives \(p(x)=x^2-49=(x-7)(x+7)\). Setting \(p(x)=0\) yields \(x=\pm7\), so the graph meets the x-axis at \((7,0)\) and \((-7,0)\). Option C is a common confusion: \((0,7)\) and \((0,-7)\) are y-intercepts, not x-intercepts. Option B would require zeros at \(x=\pm49\) which correspond to \(x^2-2401\), not our polynomial. Exam tip: to find x-intercepts set \(p(x)=0\) and factor; recognize difference of squares 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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