If (p(x)=mx+n), (p(0)=-6) and (p(4)=18), what is (m+n)?
Answer and explanation
Correct answer: 0
Given \(p(x)=mx+n\). Substituting \(x=0\), we get \(p(0)=n=-6\). Also, \(p(4)=18\) gives \(4m+n=18\), so \(4m-6=18\). Hence \(4m=24\) and \(m=6\). Therefore, \(m+n=6+(-6)=0\). Option 6 is only the value of \(m\), not of \(m+n\). Exam tip: for a linear polynomial, \(p(0)\) directly gives the constant term \(n\).
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What is the correct answer to this question?
0
Why is this the correct answer?
Given \(p(x)=mx+n\). Substituting \(x=0\), we get \(p(0)=n=-6\). Also, \(p(4)=18\) gives \(4m+n=18\), so \(4m-6=18\). Hence \(4m=24\) and \(m=6\). Therefore, \(m+n=6+(-6)=0\). Option 6 is only the value of \(m\), not of \(m+n\). Exam tip: for a linear polynomial, \(p(0)\) directly gives the constant term \(n\).
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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