If p(x) = (x + 2)(x − 7), at which points will the graph meet the x-axis?
Answer and explanation
Correct answer: (−2, 0) and (7, 0)
The graph meets the x-axis when the polynomial value is zero. In factored form, p(x) = (x + 2)(x − 7), so the product is zero when either factor is zero. From x + 2 = 0, we get x = −2; from x − 7 = 0, we get x = 7. The corresponding x-axis points must have y-coordinate 0, giving (−2, 0) and (7, 0). Therefore option B is correct. Option A reverses the signs of both roots. Option C writes the values as y-coordinates on the y-axis, and option D pairs the roots with nonzero y-coordinates, so neither represents x-axis intersections.
Frequently asked questions
What is the correct answer to this question?
(−2, 0) and (7, 0)
Why is this the correct answer?
The graph meets the x-axis when the polynomial value is zero. In factored form, p(x) = (x + 2)(x − 7), so the product is zero when either factor is zero. From x + 2 = 0, we get x = −2; from x − 7 = 0, we get x = 7. The corresponding x-axis points must have y-coordinate 0, giving (−2, 0) and (7, 0). Therefore option B is correct. Option A reverses the signs of both roots. Option C writes the values as y-coordinates on the y-axis, and option D pairs the roots with nonzero y-coordinates, so neither represents x-axis intersections.
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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