If p(x) = x³ − 9x² + 18x, what is the mean of the zeroes of the graph?
Answer and explanation
Correct answer: 3
The zeroes are the x-values at which the polynomial graph meets the x-axis. Factor the expression: p(x) = x³ − 9x² + 18x = x(x² − 9x + 18) = x(x − 3)(x − 6). Thus the three zeroes are 0, 3, and 6. Their mean is (0 + 3 + 6)/3 = 9/3 = 3. Therefore option A is correct. The value 6 is one zero, and 9 is the sum of the zeroes, not their mean. Although 18/3 equals 6, it also does not equal the required average; the constant 18 is not the sum of all zeroes.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The zeroes are the x-values at which the polynomial graph meets the x-axis. Factor the expression: p(x) = x³ − 9x² + 18x = x(x² − 9x + 18) = x(x − 3)(x − 6). Thus the three zeroes are 0, 3, and 6. Their mean is (0 + 3 + 6)/3 = 9/3 = 3. Therefore option A is correct. The value 6 is one zero, and 9 is the sum of the zeroes, not their mean. Although 18/3 equals 6, it also does not equal the required average; the constant 18 is not the sum of all zeroes.
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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