For which value will ((3r-12)x+5) not remain a linear polynomial?
Answer and explanation
Correct answer: \(r=4\)
For a polynomial to be linear, the coefficient of \(x\) must not be zero. Here, the coefficient of \(x\) is \(3r-12\). For the expression to stop being linear, \(3r-12=0\), which gives \(r=4\). At this value, the expression becomes \(5\), a constant polynomial. For the nearby option \(r=3\), the coefficient is \(-3\), so it is still linear. Exam tip: In a parameter-based polynomial, set the coefficient of the highest power to zero to check when its degree decreases.
Frequently asked questions
What is the correct answer to this question?
\(r=4\)
Why is this the correct answer?
For a polynomial to be linear, the coefficient of \(x\) must not be zero. Here, the coefficient of \(x\) is \(3r-12\). For the expression to stop being linear, \(3r-12=0\), which gives \(r=4\). At this value, the expression becomes \(5\), a constant polynomial. For the nearby option \(r=3\), the coefficient is \(-3\), so it is still linear. Exam tip: In a parameter-based polynomial, set the coefficient of the highest power to zero to check when its degree decreases.
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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