If (\alpha) and (\beta) are the roots of the equation (x^2-9x+18=0), what is the value of ((\alpha-3)(\beta-3))?
Answer and explanation
Correct answer: 0
By Vieta’s formulas, (\alpha+\beta=9) and (\alpha\beta=18). Therefore, ((\alpha-3)(\beta-3)=\alpha\beta-3(\alpha+\beta)+9=18-3(9)+9=0). Hence, option A is correct. Exam tip: expand the product carefully; subtracting 3 from each root introduces the middle term (-3(\alpha+\beta)), which is often missed.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
By Vieta’s formulas, (\alpha+\beta=9) and (\alpha\beta=18). Therefore, ((\alpha-3)(\beta-3)=\alpha\beta-3(\alpha+\beta)+9=18-3(9)+9=0). Hence, option A is correct. Exam tip: expand the product carefully; subtracting 3 from each root introduces the middle term (-3(\alpha+\beta)), which is often missed.
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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