What are the roots of the equation \(x^2+8x+5=0\)?
Answer and explanation
Correct answer: \(x=-4\pm\sqrt{11}\)
Completing the square in \(x^2+8x+5=0\) gives \(x^2+8x+16=11\), or \((x+4)^2=11\). Hence, \(x+4=\pm\sqrt{11}\), so the roots are \(x=-4\pm\sqrt{11}\). Option B has the wrong sign before 4, while option D incorrectly omits the square-root sign. Exam tip: the \(\pm\) symbol represents both roots, so write both values when required.
Frequently asked questions
What is the correct answer to this question?
\(x=-4\pm\sqrt{11}\)
Why is this the correct answer?
Completing the square in \(x^2+8x+5=0\) gives \(x^2+8x+16=11\), or \((x+4)^2=11\). Hence, \(x+4=\pm\sqrt{11}\), so the roots are \(x=-4\pm\sqrt{11}\). Option B has the wrong sign before 4, while option D incorrectly omits the square-root sign. Exam tip: the \(\pm\) symbol represents both roots, so write both values when required.
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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