If p(x) = x² − 19x + 90, what is the distance between the zeroes of the graph?
Answer and explanation
Correct answer: 1
The graph’s zeroes are its x-axis intercepts. Factor the quadratic by finding two numbers whose product is 90 and whose sum is 19: x² − 19x + 90 = (x − 9)(x − 10). Hence the zeroes are x = 9 and x = 10. The distance between them on the x-axis is |10 − 9| = 1 unit, so option A is correct. The number 19 is the sum of the zeroes according to the coefficient relation, and 90 is their product. The value 9 is one zero only, not the distance separating the two intercepts.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The graph’s zeroes are its x-axis intercepts. Factor the quadratic by finding two numbers whose product is 90 and whose sum is 19: x² − 19x + 90 = (x − 9)(x − 10). Hence the zeroes are x = 9 and x = 10. The distance between them on the x-axis is |10 − 9| = 1 unit, so option A is correct. The number 19 is the sum of the zeroes according to the coefficient relation, and 90 is their product. The value 9 is one zero only, not the distance separating the two intercepts.
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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