If \\(x+a)^2=x^2+10x+25\\) is an identity, what is the value of \\(a\\)?
Answer and explanation
Correct answer: 5
Expanding gives \\(x+a)^2=x^2+2ax+a^2\\). Comparing the coefficients of \\(x\\) on both sides, \\(2a=10\\), so \\(a=5\\). Option B is incorrect because \\(a=-5\\) would make the coefficient of \\(x\\) equal to \\(-10\\). Exam tip: In an identity, compare the coefficients of like powers of the variable.
Frequently asked questions
What is the correct answer to this question?
5
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=10\\), so \\(a=5\\). Option B is incorrect because \\(a=-5\\) would make the coefficient of \\(x\\) equal to \\(-10\\). Exam tip: In an identity, compare the 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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