Which of the following is the correct pair of roots of the quadratic equation \(x^2-(2m+3)x+(m+1)(m+2)=0\)?
Answer and explanation
Correct answer: \(m+1\) and \(m+2\)
If the roots are \(\alpha\) and \(\beta\), Vieta’s formulas give \(\alpha+\beta=2m+3\) and \(\alpha\beta=(m+1)(m+2)\). For option A, \((m+1)+(m+2)=2m+3\), and the product is exactly \((m+1)(m+2)\). Hence the roots are \(m+1\) and \(m+2\). Exam tip: compare the sum and product of the proposed roots with the coefficients of the quadratic.
Frequently asked questions
What is the correct answer to this question?
\(m+1\) and \(m+2\)
Why is this the correct answer?
If the roots are \(\alpha\) and \(\beta\), Vieta’s formulas give \(\alpha+\beta=2m+3\) and \(\alpha\beta=(m+1)(m+2)\). For option A, \((m+1)+(m+2)=2m+3\), and the product is exactly \((m+1)(m+2)\). Hence the roots are \(m+1\) and \(m+2\). Exam tip: compare the sum and product of the proposed roots with the coefficients of the quadratic.
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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