If a graph cuts the x-axis at -7 and -2, what are the solutions of p(x) = 0?
Answer and explanation
Correct answer: -7 and -2
A solution of p(x) = 0 is an x-value for which the graph has y-coordinate zero. Such points are precisely the intersections of the graph with the x-axis. The stated intersections have x-coordinates -7 and -2, so p(-7) = 0 and p(-2) = 0. Hence the solution set is {-7, -2}, represented by option A. The negative signs must be retained because they are the actual x-coordinates of the intercepts; changing them to 7 and 2 gives different points on the opposite side of the y-axis. Option C keeps only one sign correct, and option D ignores the two explicitly given x-axis intersections. No calculation beyond reading the graph is needed.
Frequently asked questions
What is the correct answer to this question?
-7 and -2
Why is this the correct answer?
A solution of p(x) = 0 is an x-value for which the graph has y-coordinate zero. Such points are precisely the intersections of the graph with the x-axis. The stated intersections have x-coordinates -7 and -2, so p(-7) = 0 and p(-2) = 0. Hence the solution set is {-7, -2}, represented by option A. The negative signs must be retained because they are the actual x-coordinates of the intercepts; changing them to 7 and 2 gives different points on the opposite side of the y-axis. Option C keeps only one sign correct, and option D ignores the two explicitly given x-axis intersections. No calculation beyond reading the graph is needed.
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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