In the graph of the polynomial p(x), where y = p(x), what is the value of y at a zero of the polynomial?
Answer and explanation
Correct answer: 0
The governing concept is the graphical meaning of a zero of a polynomial. A number r is called a zero of p(x) when p(r) = 0. On the graph y = p(x), the point corresponding to x = r therefore has coordinates (r, p(r)) = (r, 0). Hence its vertical coordinate, or y-value, is zero. Geometrically, every real zero is represented by a point where the polynomial graph meets or touches the x-axis. The options 1 and -1 are possible y-values at other points, but not at a zero. The value cannot be undetermined because the defining condition of a zero itself fixes p(r) as 0.
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Why is this the correct answer?
The governing concept is the graphical meaning of a zero of a polynomial. A number r is called a zero of p(x) when p(r) = 0. On the graph y = p(x), the point corresponding to x = r therefore has coordinates (r, p(r)) = (r, 0). Hence its vertical coordinate, or y-value, is zero. Geometrically, every real zero is represented by a point where the polynomial graph meets or touches the x-axis. The options 1 and -1 are possible y-values at other points, but not at a zero. The value cannot be undetermined because the defining condition of a zero itself fixes p(r) as 0.
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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