If a graph cuts the x-axis at x = -12, x = -3 and x = 8, what is the range of the zeroes?
Answer and explanation
Correct answer: 20
The governing concept is the range of a finite set of real numbers, calculated as the greatest value minus the least value. The zeroes given by the x-intercepts are -12, -3 and 8. The greatest zero is 8 and the least zero is -12. Therefore, range = maximum - minimum = 8 - (-12) = 8 + 12 = 20. Hence option C is correct. The value 11 is the difference between -12 and -3, while 15 is the difference between -3 and 12 only by an incorrect sign interpretation. Option D gives -20, but a range is a non-negative spread and cannot be negative. The middle zero does not affect the maximum-minus-minimum calculation.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
The governing concept is the range of a finite set of real numbers, calculated as the greatest value minus the least value. The zeroes given by the x-intercepts are -12, -3 and 8. The greatest zero is 8 and the least zero is -12. Therefore, range = maximum - minimum = 8 - (-12) = 8 + 12 = 20. Hence option C is correct. The value 11 is the difference between -12 and -3, while 15 is the difference between -3 and 12 only by an incorrect sign interpretation. Option D gives -20, but a range is a non-negative spread and cannot be negative. The middle zero does not affect the maximum-minus-minimum calculation.
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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