What is the correct condition for (a) in the linear polynomial (ax+b)?
Answer and explanation
Correct answer: \(a\neq 0\)
The polynomial \(ax+b\) is linear only if the coefficient of \(x\), namely \(a\), is non-zero. Then the highest power of \(x\) is 1, so the polynomial has degree 1. If \(a=0\), the expression becomes \(b\), which is a constant polynomial, not a linear polynomial. Exam tip: while finding a polynomial’s degree, ensure that the coefficient of the highest-power term is non-zero.
Frequently asked questions
What is the correct answer to this question?
\(a\neq 0\)
Why is this the correct answer?
The polynomial \(ax+b\) is linear only if the coefficient of \(x\), namely \(a\), is non-zero. Then the highest power of \(x\) is 1, so the polynomial has degree 1. If \(a=0\), the expression becomes \(b\), which is a constant polynomial, not a linear polynomial. Exam tip: while finding a polynomial’s degree, ensure that the coefficient of the highest-power term is non-zero.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear polynomials.
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