If the identity \\((x+a)^2=x^2-20x+100\\) is true for all \\(x\\), what is the value of \\(a\\)?
Answer and explanation
Correct answer: \\(-10\\)
Expanding gives \\((x+a)^2=x^2+2ax+a^2\\). Comparing the coefficients of \\(x\\) on both sides, \\(2a=-20\\), so \\(a=-10\\). Substituting this value also gives \\(a^2=100\\), confirming the constant term. Exam tip: For an identity, compare coefficients of like powers of the variable.
Frequently asked questions
What is the correct answer to this question?
\\(-10\\)
Why is this the correct answer?
Expanding gives \\((x+a)^2=x^2+2ax+a^2\\). Comparing the coefficients of \\(x\\) on both sides, \\(2a=-20\\), so \\(a=-10\\). Substituting this value also gives \\(a^2=100\\), confirming the constant term. 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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