If the graph of a polynomial is parallel to the x-axis and does not intersect it, how many zeroes does the polynomial have?
Answer and explanation
Correct answer: Zero
A graph parallel to the x-axis is a horizontal line of the form \(y=c\). If it does not intersect the x-axis then \(c\neq 0\). Roots are solutions of \(p(x)=0\); here the polynomial equals the nonzero constant \(c\), so there is no solution and hence zero zeroes. The distractor "one" would apply if the graph merely touched the x-axis (a single root), while "infinite" applies when \(c=0\) (the graph lies on the x-axis and every x is a root). Exam tip: for horizontal lines check whether the constant equals zero to decide roots.
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What is the correct answer to this question?
Zero
Why is this the correct answer?
A graph parallel to the x-axis is a horizontal line of the form \(y=c\). If it does not intersect the x-axis then \(c\neq 0\). Roots are solutions of \(p(x)=0\); here the polynomial equals the nonzero constant \(c\), so there is no solution and hence zero zeroes. The distractor "one" would apply if the graph merely touched the x-axis (a single root), while "infinite" applies when \(c=0\) (the graph lies on the x-axis and every x is a root). Exam tip: for horizontal lines check whether the constant equals zero to decide roots.
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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