What are the roots of the equation \(x^2+4x+1=0\)?
Answer and explanation
Correct answer: \(x=-2\pm\sqrt{3}\)
Rewrite the equation by completing the square: \(x^2+4x+1=0\Rightarrow x^2+4x+4=3\Rightarrow (x+2)^2=3\). Thus, \(x+2=\pm\sqrt{3}\), giving \(x=-2\pm\sqrt{3}\). Option B has the wrong sign for the constant term in the solution. In an exam, remember that \(\pm\) represents both roots.
Frequently asked questions
What is the correct answer to this question?
\(x=-2\pm\sqrt{3}\)
Why is this the correct answer?
Rewrite the equation by completing the square: \(x^2+4x+1=0\Rightarrow x^2+4x+4=3\Rightarrow (x+2)^2=3\). Thus, \(x+2=\pm\sqrt{3}\), giving \(x=-2\pm\sqrt{3}\). Option B has the wrong sign for the constant term in the solution. In an exam, remember that \(\pm\) represents both roots.
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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