What will be the x-axis intersections of the graph of p(x) = (x − 4)(x + 2)?
Answer and explanation
Correct answer: (4, 0) and (−2, 0)
An x-axis intersection occurs when y = p(x) = 0. For p(x) = (x − 4)(x + 2), the product is zero when either factor is zero. Thus x − 4 = 0 gives x = 4, and x + 2 = 0 gives x = −2. Each zero x-coordinate is paired with y = 0, so the intersections are (4, 0) and (−2, 0). Option B reverses the signs and therefore gives the wrong zeroes. Option C lists y-axis points because their first coordinate is 0, and Option D uses the two numbers as y-coordinates rather than forming points on the x-axis. Hence Option A is correct.
Frequently asked questions
What is the correct answer to this question?
(4, 0) and (−2, 0)
Why is this the correct answer?
An x-axis intersection occurs when y = p(x) = 0. For p(x) = (x − 4)(x + 2), the product is zero when either factor is zero. Thus x − 4 = 0 gives x = 4, and x + 2 = 0 gives x = −2. Each zero x-coordinate is paired with y = 0, so the intersections are (4, 0) and (−2, 0). Option B reverses the signs and therefore gives the wrong zeroes. Option C lists y-axis points because their first coordinate is 0, and Option D uses the two numbers as y-coordinates rather than forming points on the x-axis. Hence Option A is correct.
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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