If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2+7x+10=0\), what is the value of \((\alpha+2)(\beta+2)\)?
Answer and explanation
Correct answer: 0
By Vieta’s formulas, \(\alpha+\beta=-\frac{7}{1}=-7\) and \(\alpha\beta=\frac{10}{1}=10\). Therefore, \((\alpha+2)(\beta+2)=\alpha\beta+2(\alpha+\beta)+4=10+2(-7)+4=0\). Option B is only the value of \(\alpha\beta\), not of the complete expression. Exam tip: For expressions involving roots, first find the sum and product of the roots using Vieta’s formulas.
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What is the correct answer to this question?
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Why is this the correct answer?
By Vieta’s formulas, \(\alpha+\beta=-\frac{7}{1}=-7\) and \(\alpha\beta=\frac{10}{1}=10\). Therefore, \((\alpha+2)(\beta+2)=\alpha\beta+2(\alpha+\beta)+4=10+2(-7)+4=0\). Option B is only the value of \(\alpha\beta\), not of the complete expression. Exam tip: For expressions involving roots, first find the sum and product of the roots using Vieta’s formulas.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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