The roots of the equation \(x^2-8x+5=0\) are \(\alpha\) and \(\beta\). What is the value of \(\alpha+\beta+4\alpha\beta\)?
Answer and explanation
Correct answer: 28
By Vieta’s formulas for \(x^2-8x+5=0\), the sum of the roots is \(\alpha+\beta=8\) and their product is \(\alpha\beta=5\). Therefore, \(\alpha+\beta+4\alpha\beta=8+4(5)=28\). Option 13 results from adding the product only once, so it is incorrect. Exam tip: for \(ax^2+bx+c=0\), the sum of roots is \(-b/a\) and the product is \(c/a\).
Frequently asked questions
What is the correct answer to this question?
28
Why is this the correct answer?
By Vieta’s formulas for \(x^2-8x+5=0\), the sum of the roots is \(\alpha+\beta=8\) and their product is \(\alpha\beta=5\). Therefore, \(\alpha+\beta+4\alpha\beta=8+4(5)=28\). Option 13 results from adding the product only once, so it is incorrect. Exam tip: for \(ax^2+bx+c=0\), the sum of roots is \(-b/a\) and the product is \(c/a\).
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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