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What is the repeated root of (x^2+14x+49=0)?
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Answer and explanation
Correct answer: \(x=-7\)
Since \(x^2+14x+49=(x+7)^2\), the equation becomes \((x+7)^2=0\), giving \(x=-7\). This root occurs twice, so it is the repeated root. Exam tip: for \((x+a)^2=0\), the root is \(x=-a\), not \(x=a\).
Frequently asked questions
What is the correct answer to this question?
\(x=-7\)
Why is this the correct answer?
Since \(x^2+14x+49=(x+7)^2\), the equation becomes \((x+7)^2=0\), giving \(x=-7\). This root occurs twice, so it is the repeated root. Exam tip: for \((x+a)^2=0\), the root is \(x=-a\), not \(x=a\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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