If (a, 0) and (b, 0) are intersection points of a graph and a < b, what is the smaller zero?
Answer and explanation
Correct answer: a
The governing concept is the geometrical meaning of a zero: a real number r is a zero of p(x) exactly when the graph y = p(x) passes through (r, 0). Thus the two points (a, 0) and (b, 0) represent the zeroes a and b, respectively. The condition a < b tells us their order on the number line, so a is the smaller value. Therefore option A is correct. The value b is the larger zero, while 0 is merely the common y-coordinate of both x-axis points and is not automatically a zero. The sum a + b combines the two zeroes but does not identify the smaller one. This reasoning applies regardless of the actual numerical values of a and b.
Frequently asked questions
What is the correct answer to this question?
a
Why is this the correct answer?
The governing concept is the geometrical meaning of a zero: a real number r is a zero of p(x) exactly when the graph y = p(x) passes through (r, 0). Thus the two points (a, 0) and (b, 0) represent the zeroes a and b, respectively. The condition a < b tells us their order on the number line, so a is the smaller value. Therefore option A is correct. The value b is the larger zero, while 0 is merely the common y-coordinate of both x-axis points and is not automatically a zero. The sum a + b combines the two zeroes but does not identify the smaller one. This reasoning applies regardless of the actual numerical values of a and b.
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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