If p(x)=x^2-11x+30, what is the distance between the zeroes of the graph?
Answer and explanation
Correct answer: 1
The governing concept is that the zeroes of a polynomial are the x-coordinates of its x-axis intersections. Factor the quadratic using two numbers whose product is 30 and whose sum is 11: x^2-11x+30 = (x-5)(x-6). Therefore the zeroes are x=5 and x=6. The distance between these points along the x-axis is the absolute difference, |6-5|=1. Thus Option A is correct. Option B is one of the zeroes, Option C is the magnitude of the coefficient of x and also the sum of the zeroes, while Option D is the product of the zeroes; none of those represents the distance.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The governing concept is that the zeroes of a polynomial are the x-coordinates of its x-axis intersections. Factor the quadratic using two numbers whose product is 30 and whose sum is 11: x^2-11x+30 = (x-5)(x-6). Therefore the zeroes are x=5 and x=6. The distance between these points along the x-axis is the absolute difference, |6-5|=1. Thus Option A is correct. Option B is one of the zeroes, Option C is the magnitude of the coefficient of x and also the sum of the zeroes, while Option D is the product of the zeroes; none of those represents the 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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