If (p(x)=mx+n), (p(-4)=3) and (p(2)=27), what is (m)?
Answer and explanation
Correct answer: \(4\)
Take the difference of the given values: \(p(2)-p(-4)=27-3=24\). For the linear polynomial \(p(x)=mx+n\), \(p(2)-p(-4)=m[2-(-4)]=6m\). Hence, \(6m=24\), so \(m=4\). The value \(24\) is the difference of the function values, not the value of \(m\). Exam tip: when values of a linear polynomial at two points are given, divide the difference in polynomial values by the difference in the corresponding \(x\)-values to find \(m\).
Frequently asked questions
What is the correct answer to this question?
\(4\)
Why is this the correct answer?
Take the difference of the given values: \(p(2)-p(-4)=27-3=24\). For the linear polynomial \(p(x)=mx+n\), \(p(2)-p(-4)=m[2-(-4)]=6m\). Hence, \(6m=24\), so \(m=4\). The value \(24\) is the difference of the function values, not the value of \(m\). Exam tip: when values of a linear polynomial at two points are given, divide the difference in polynomial values by the difference in the corresponding \(x\)-values to find \(m\).
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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