What are the roots of the equation \(x^2+10x+6=0\)?
Answer and explanation
Correct answer: \(x=-5\pm\sqrt{19}\)
Here, \(a=1, b=10, c=6\). Using the quadratic formula, \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-10\pm\sqrt{100-24}}{2}=\frac{-10\pm\sqrt{76}}{2}=-5\pm\sqrt{19}\). Therefore, option A is correct. Option B has the wrong sign for \(-b\), while option D omits the square root of the simplified discriminant. Exam tip: verify that the sum of the roots is \(-10\) and their product is \(6\).
Frequently asked questions
What is the correct answer to this question?
\(x=-5\pm\sqrt{19}\)
Why is this the correct answer?
Here, \(a=1, b=10, c=6\). Using the quadratic formula, \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-10\pm\sqrt{100-24}}{2}=\frac{-10\pm\sqrt{76}}{2}=-5\pm\sqrt{19}\). Therefore, option A is correct. Option B has the wrong sign for \(-b\), while option D omits the square root of the simplified discriminant. Exam tip: verify that the sum of the roots is \(-10\) and their product is \(6\).
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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