If p(x) = x^2 - 13x + 42, what is the distance between the zeroes of the graph?
Answer and explanation
Correct answer: 1
The governing idea is that the zeroes of a polynomial are the x-coordinates of the points where its graph meets the x-axis. Factor the quadratic: x^2 - 13x + 42 = (x - 6)(x - 7), because 6 × 7 = 42 and 6 + 7 = 13. Hence the zeroes are x = 6 and x = 7. Their distance on the number line is the absolute difference, |7 - 6| = 1. Therefore, option A is correct. The numbers 6 and 7 are the zeroes, not their distance; 13 is related to their sum, and 42 is their product. Thus options B, C and D confuse intermediate relationships with the requested distance.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The governing idea is that the zeroes of a polynomial are the x-coordinates of the points where its graph meets the x-axis. Factor the quadratic: x^2 - 13x + 42 = (x - 6)(x - 7), because 6 × 7 = 42 and 6 + 7 = 13. Hence the zeroes are x = 6 and x = 7. Their distance on the number line is the absolute difference, |7 - 6| = 1. Therefore, option A is correct. The numbers 6 and 7 are the zeroes, not their distance; 13 is related to their sum, and 42 is their product. Thus options B, C and D confuse intermediate relationships with the requested distance.
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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