If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-8x+12=0\), what is the value of \((\alpha+2)(\beta+2)\)?
Answer and explanation
Correct answer: 32
By Vieta’s formulas, \(\alpha+\beta=\frac{8}{1}=8\) and \(\alpha\beta=\frac{12}{1}=12\). Therefore, \((\alpha+2)(\beta+2)=\alpha\beta+2(\alpha+\beta)+4=12+2(8)+4=32\). Hence, the correct answer is 32. In the exam, remember to include the middle term \(2(\alpha+\beta)\) when expanding the product.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
By Vieta’s formulas, \(\alpha+\beta=\frac{8}{1}=8\) and \(\alpha\beta=\frac{12}{1}=12\). Therefore, \((\alpha+2)(\beta+2)=\alpha\beta+2(\alpha+\beta)+4=12+2(8)+4=32\). Hence, the correct answer is 32. In the exam, remember to include the middle term \(2(\alpha+\beta)\) when expanding the product.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
