If (p(-8)=0), (p(-2)>0), (p(3)=0) and (p(9)<0), what is the sum of the given zeroes?
Answer and explanation
Correct answer: (-5)
A zero is an input x for which the polynomial value is exactly zero. Positive or negative values do not represent zeroes; they only show that the graph lies above or below the x-axis at those inputs. Therefore, in a list of function values, we select only the statements written with equality to 0.
Here \(p(-8)=0\), so -8 is a zero, and \(p(3)=0\), so 3 is another zero. The statements \(p(-2)>0\) and \(p(9)<0\) do not add zeroes. Their sum is \((-8)+3=-5\). Therefore option A is correct. A common mistake is to use the signs or to include every listed input instead of checking which function values are exactly zero.
Frequently asked questions
What is the correct answer to this question?
(-5)
Why is this the correct answer?
A zero is an input x for which the polynomial value is exactly zero. Positive or negative values do not represent zeroes; they only show that the graph lies above or below the x-axis at those inputs. Therefore, in a list of function values, we select only the statements written with equality to 0.
Here \(p(-8)=0\), so -8 is a zero, and \(p(3)=0\), so 3 is another zero. The statements \(p(-2)>0\) and \(p(9)<0\) do not add zeroes. Their sum is \((-8)+3=-5\). Therefore option A is correct. A common mistake is to use the signs or to include every listed input instead of checking which function values are exactly zero.
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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