If \\(x+a\\)^2=x^2+18x+81 is an identity, what is the value of \\(a\\)?
Answer and explanation
Correct answer: 9
Expanding gives \\(x+a\\)^2=x^2+2ax+a^2"). Comparing the coefficients of \\(x\\), we get \\(2a=18\\), so \\(a=9\\). This also satisfies the constant-term condition \\(a^2=81\\). Although \\(-9\\) gives the same constant term, it makes the coefficient of \\(x\\) equal to \\(-18\\), so it is incorrect. Exam tip: For an identity, compare coefficients of like powers on both sides.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
Expanding gives \\(x+a\\)^2=x^2+2ax+a^2"). Comparing the coefficients of \\(x\\), we get \\(2a=18\\), so \\(a=9\\). This also satisfies the constant-term condition \\(a^2=81\\). Although \\(-9\\) gives the same constant term, it makes the coefficient of \\(x\\) equal to \\(-18\\), so it is incorrect. Exam tip: For an identity, compare coefficients of like powers on both sides.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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