If \(p(x)=x^2-2x-8\), at which points does its graph intersect the x-axis?
Answer and explanation
Correct answer: (-2,0) and (4,0)
Points where the graph meets the x-axis are the zeros of \(p(x)\), so set \(p(x)=0\). Factor: \(x^2-2x-8=(x-4)(x+2)\). Therefore \(x=4\) and \(x=-2\), giving points \((4,0)\) and \((-2,0)\). Option B has signs swapped (gives wrong x-values); option C lists points on the y-axis, not x-axis; option D is just incorrect roots. Exam tip: set the quadratic equal to zero and factor or use the quadratic formula; then report roots as (x,0).
Frequently asked questions
What is the correct answer to this question?
(-2,0) and (4,0)
Why is this the correct answer?
Points where the graph meets the x-axis are the zeros of \(p(x)\), so set \(p(x)=0\). Factor: \(x^2-2x-8=(x-4)(x+2)\). Therefore \(x=4\) and \(x=-2\), giving points \((4,0)\) and \((-2,0)\). Option B has signs swapped (gives wrong x-values); option C lists points on the y-axis, not x-axis; option D is just incorrect roots. Exam tip: set the quadratic equal to zero and factor or use the quadratic formula; then report roots as (x,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..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
