Is \(x=-2\) a root of the equation \(x^2+3x+2=0\)?
Answer and explanation
Correct answer: Yes
Substituting \(x=-2\) gives \((-2)^2+3(-2)+2 = 4-6+2 = 0\), so \(x=-2\) is indeed a root. Factoring yields \(x^2+3x+2=(x+1)(x+2)\), so the real roots are \(x=-1\) and \(x=-2\). Thus 'Only at \(x=2\)' is incorrect because \(+2\) is not a root, and 'No real root' is also incorrect. Exam tip: either substitute carefully (watch signs) or factor the quadratic to find/check roots quickly.
Frequently asked questions
What is the correct answer to this question?
Yes
Why is this the correct answer?
Substituting \(x=-2\) gives \((-2)^2+3(-2)+2 = 4-6+2 = 0\), so \(x=-2\) is indeed a root. Factoring yields \(x^2+3x+2=(x+1)(x+2)\), so the real roots are \(x=-1\) and \(x=-2\). Thus 'Only at \(x=2\)' is incorrect because \(+2\) is not a root, and 'No real root' is also incorrect. Exam tip: either substitute carefully (watch signs) or factor the quadratic to find/check roots quickly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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