If on a graph (p(-5)>0), (p(-2)=0), (p(1)<0), (p(6)=0), what is the sum of the zeroes among the given values?
Answer and explanation
Correct answer: (4)
A value is a zero of \(p(x)\) only when the function value at that input is exactly 0. Statements such as \(p(-5)>0\) and \(p(1)<0\) describe points above and below the x-axis, respectively; they do not make -5 or 1 zeroes. The equalities \(p(x)=0\), on the other hand, directly identify zeroes.
From \(p(-2)=0\), the value \(-2\) is a zero. From \(p(6)=0\), the value 6 is another zero. Their sum is \((-2)+6=4\). Hence option A is correct. It would be an error to add all four listed x-values, because the inequality signs show only the position relative to the axis, not an x-axis intersection.
Frequently asked questions
What is the correct answer to this question?
(4)
Why is this the correct answer?
A value is a zero of \(p(x)\) only when the function value at that input is exactly 0. Statements such as \(p(-5)>0\) and \(p(1)<0\) describe points above and below the x-axis, respectively; they do not make -5 or 1 zeroes. The equalities \(p(x)=0\), on the other hand, directly identify zeroes.
From \(p(-2)=0\), the value \(-2\) is a zero. From \(p(6)=0\), the value 6 is another zero. Their sum is \((-2)+6=4\). Hence option A is correct. It would be an error to add all four listed x-values, because the inequality signs show only the position relative to the axis, not an x-axis intersection.
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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