If (p(x)=mx+n), (p(-1)=3) and (p(4)=23), what is (m+n)?
Answer and explanation
Correct answer: 11
Given \(p(x)=mx+n\), we get \(p(-1)=-m+n=3\) and \(p(4)=4m+n=23\). Subtracting the first equation from the second gives \(5m=20\), so \(m=4\). Then \(-4+n=3\) gives \(n=7\). Therefore, \(m+n=4+7=11\). Option 7 is only the value of \(n\), not of \(m+n\). Exam tip: Convert each given value of a linear polynomial into an equation before solving.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
Given \(p(x)=mx+n\), we get \(p(-1)=-m+n=3\) and \(p(4)=4m+n=23\). Subtracting the first equation from the second gives \(5m=20\), so \(m=4\). Then \(-4+n=3\) gives \(n=7\). Therefore, \(m+n=4+7=11\). Option 7 is only the value of \(n\), not of \(m+n\). Exam tip: Convert each given value of a linear polynomial into an equation before solving.
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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