If \(p(-3)=0\), \(p(2)=5\) and \(p(8)=0\), at which points does the graph intersect the x-axis?
Answer and explanation
Correct answer: (-3,0) and (8,0)
Intersections with the x-axis occur where \(p(x)=0\). Since \(p(-3)=0\) and \(p(8)=0\), the x-intercepts are (-3,0) and (8,0). Because \(p(2)=5\) ≠ 0, the point (2,5) is not an x-intercept. Exam tip: to find x-intercepts from function values, look for input values that give output 0 (roots).
Frequently asked questions
What is the correct answer to this question?
(-3,0) and (8,0)
Why is this the correct answer?
Intersections with the x-axis occur where \(p(x)=0\). Since \(p(-3)=0\) and \(p(8)=0\), the x-intercepts are (-3,0) and (8,0). Because \(p(2)=5\) ≠ 0, the point (2,5) is not an x-intercept. Exam tip: to find x-intercepts from function values, look for input values that give output 0 (roots).
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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