If p(x) = x² − 17x + 72, what is the distance between the zeroes of the graph?
Answer and explanation
Correct answer: 1
The zeroes of a polynomial are the x-coordinates where its graph meets the x-axis. Factor the quadratic: x² − 17x + 72 = (x − 8)(x − 9), because 8 × 9 = 72 and 8 + 9 = 17. Therefore, the two zeroes are x = 8 and x = 9. Their distance on the x-axis is the absolute difference |9 − 8| = 1 unit. Thus option A is correct. The number 17 is the sum of the zeroes, while 72 is their product; neither represents the distance. Option B is one zero, not the separation between them.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The zeroes of a polynomial are the x-coordinates where its graph meets the x-axis. Factor the quadratic: x² − 17x + 72 = (x − 8)(x − 9), because 8 × 9 = 72 and 8 + 9 = 17. Therefore, the two zeroes are x = 8 and x = 9. Their distance on the x-axis is the absolute difference |9 − 8| = 1 unit. Thus option A is correct. The number 17 is the sum of the zeroes, while 72 is their product; neither represents the distance. Option B is one zero, not the separation between them.
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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