If \\(x+a\\)^2 = x^2 - 12x + 36 holds for all real x, what is the value of a?
Answer and explanation
Correct answer: -6
Expanding gives \\(x+a\\)^2 = x^2 + 2ax + a^2\\). Comparing the coefficients of x, \\(2a=-12\\), so \\(a=-6\\). The constant term gives \\(a^2=36\\), which alone allows both 6 and -6; the coefficient of x identifies -6 uniquely. Exam tip: For an identity, compare coefficients of like powers of the variable.
Frequently asked questions
What is the correct answer to this question?
-6
Why is this the correct answer?
Expanding gives \\(x+a\\)^2 = x^2 + 2ax + a^2\\). Comparing the coefficients of x, \\(2a=-12\\), so \\(a=-6\\). The constant term gives \\(a^2=36\\), which alone allows both 6 and -6; the coefficient of x identifies -6 uniquely. Exam tip: For an identity, compare coefficients of like powers of the variable.
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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