If \(p(-3)=0\), \(p(0)=5\) and \(p(4)=0\), at which points will the graph intersect the x-axis?
Answer and explanation
Correct answer: (-3,0) and (4,0)
An x-intercept occurs where the function value is zero, i.e. \(p(x)=0\). Here \(p(-3)=0\) and \(p(4)=0\), so the graph meets the x-axis at \((-3,0)\) and \((4,0)\). Option A is the closest distractor because it incorrectly treats \(p(0)=5\) as an x-intercept by listing \((0,5)\), but y=5≠0 so it is not on the x-axis. Exam tip: whenever you have \(p(a)=0\), record the intercept as \((a,0)\).
Frequently asked questions
What is the correct answer to this question?
(-3,0) and (4,0)
Why is this the correct answer?
An x-intercept occurs where the function value is zero, i.e. \(p(x)=0\). Here \(p(-3)=0\) and \(p(4)=0\), so the graph meets the x-axis at \((-3,0)\) and \((4,0)\). Option A is the closest distractor because it incorrectly treats \(p(0)=5\) as an x-intercept by listing \((0,5)\), but y=5≠0 so it is not on the x-axis. Exam tip: whenever you have \(p(a)=0\), record the intercept as \((a,0)\).
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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