How many real zeros does the constant polynomial \(p(x)=5\) have?
Answer and explanation
Correct answer: Zero
To find zeros set \(p(x)=0\). For \(p(x)=5\) this gives \(5=0\), which is impossible, so there are no real roots. Geometrically the graph \(y=5\) is a horizontal line that does not meet the x-axis. Note the contrast: the zero polynomial \(p(x)=0\) has every real number as a root (infinitely many). Exam tip: always solve \(p(x)=0\) to determine number of zeros and check if the polynomial is the zero polynomial first.
Frequently asked questions
What is the correct answer to this question?
Zero
Why is this the correct answer?
To find zeros set \(p(x)=0\). For \(p(x)=5\) this gives \(5=0\), which is impossible, so there are no real roots. Geometrically the graph \(y=5\) is a horizontal line that does not meet the x-axis. Note the contrast: the zero polynomial \(p(x)=0\) has every real number as a root (infinitely many). Exam tip: always solve \(p(x)=0\) to determine number of zeros and check if the polynomial is the zero polynomial first.
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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