If in a square model \(x^2+ax+36\) is a perfect square and (a) is positive, what is the value of (a)?
Answer and explanation
Correct answer: 12
Since \(36=6^2\), the perfect-square expression must be \((x+6)^2\). Expanding it gives \((x+6)^2=x^2+12x+36\). Therefore, \(a=12\). Here, \(6\) is only the square root of the constant term, not the coefficient of the middle term. Exam tip: in \((x+b)^2=x^2+2bx+b^2\), the coefficient of the middle term is always \(2b\).
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Since \(36=6^2\), the perfect-square expression must be \((x+6)^2\). Expanding it gives \((x+6)^2=x^2+12x+36\). Therefore, \(a=12\). Here, \(6\) is only the square root of the constant term, not the coefficient of the middle term. Exam tip: in \((x+b)^2=x^2+2bx+b^2\), the coefficient of the middle term is always \(2b\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.
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