If (p(x)=ax+10) and (p(2)=p(5)-15), what is (a)?
Answer and explanation
Correct answer: 5
Given \(p(x)=ax+10\), we have \(p(2)=2a+10\) and \(p(5)=5a+10\). Using \(p(2)=p(5)-15\), \(2a+10=5a+10-15\), so \(2a=5a-15\). Hence \(3a=15\), giving \(a=5\). For example, \(a=3\) does not satisfy the given condition. Exam tip: first substitute the stated values of \(x\) into the polynomial, then form and solve the equation.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Given \(p(x)=ax+10\), we have \(p(2)=2a+10\) and \(p(5)=5a+10\). Using \(p(2)=p(5)-15\), \(2a+10=5a+10-15\), so \(2a=5a-15\). Hence \(3a=15\), giving \(a=5\). For example, \(a=3\) does not satisfy the given condition. Exam tip: first substitute the stated values of \(x\) into the polynomial, then form and solve the equation.
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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