If p(x)=ax+b is linear, how should the coefficient of x be?
Answer and explanation
Correct answer: It should not be zero
For p(x)=ax+b to be a linear polynomial in x, its degree must be exactly 1. This happens only when the coefficient a of x is nonzero. If a=0, then p(x)=b, which is a constant polynomial of degree 0, not a linear polynomial. There is no requirement that a must equal 1; values such as 2, -3, or 1/2 all produce linear polynomials when used with x. Also, a does not have to equal b, because the constant term can be independent of the coefficient of x. Therefore option B is correct: a must not be zero.
Frequently asked questions
What is the correct answer to this question?
It should not be zero
Why is this the correct answer?
For p(x)=ax+b to be a linear polynomial in x, its degree must be exactly 1. This happens only when the coefficient a of x is nonzero. If a=0, then p(x)=b, which is a constant polynomial of degree 0, not a linear polynomial. There is no requirement that a must equal 1; values such as 2, -3, or 1/2 all produce linear polynomials when used with x. Also, a does not have to equal b, because the constant term can be independent of the coefficient of x. Therefore option B is correct: a must not be 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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