The roots of the equation \\(x^2-5x+2=0\\) are \\(\\alpha\\) and \\(\\beta\\). What is the value of \\(\\alpha+\\beta+2\\alpha\\beta\\)?
Answer and explanation
Correct answer: 9
For a quadratic equation \\(ax^2+bx+c=0\\), the sum of the roots is \\( -b/a \\) and their product is \\(c/a\\). Here, \\(a=1,b=-5,c=2\\), so \\(\\alpha+\\beta=5\\) and \\(\\alpha\\beta=2\\). Therefore, \\(\\alpha+\\beta+2\\alpha\\beta=5+2(2)=9\\). Exam tip: use the sum and product of roots directly instead of solving for the individual roots.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
For a quadratic equation \\(ax^2+bx+c=0\\), the sum of the roots is \\( -b/a \\) and their product is \\(c/a\\). Here, \\(a=1,b=-5,c=2\\), so \\(\\alpha+\\beta=5\\) and \\(\\alpha\\beta=2\\). Therefore, \\(\\alpha+\\beta+2\\alpha\\beta=5+2(2)=9\\). Exam tip: use the sum and product of roots directly instead of solving for the individual roots.
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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