If (p(x)=kx-8) and (p(5)=p(-1)), when will (p(x)) remain linear?
Answer and explanation
Correct answer: Never
Given \(p(5)=p(-1)\), we get \(5k-8=-k-8\). Hence \(6k=0\), so \(k=0\). Then \(p(x)=-8\) is a constant polynomial of degree 0, not a linear polynomial. In option B, \(k\ne0\) would make the polynomial linear, but it would not satisfy \(p(5)=p(-1)\). Exam tip: \(ax+b\) is linear only when \(a\ne0\).
Frequently asked questions
What is the correct answer to this question?
Never
Why is this the correct answer?
Given \(p(5)=p(-1)\), we get \(5k-8=-k-8\). Hence \(6k=0\), so \(k=0\). Then \(p(x)=-8\) is a constant polynomial of degree 0, not a linear polynomial. In option B, \(k\ne0\) would make the polynomial linear, but it would not satisfy \(p(5)=p(-1)\). Exam tip: \(ax+b\) is linear only when \(a\ne0\).
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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