If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-12x+35=0\), what is the value of \((\alpha-5)(\beta-5)\)?
Answer and explanation
Correct answer: 0
By Vieta’s formulas, \(\alpha+\beta=12\) and \(\alpha\beta=35\). Therefore, \((\alpha-5)(\beta-5)=\alpha\beta-5(\alpha+\beta)+25=35-5(12)+25=0\). Hence, option A is correct. Exam tip: For expressions involving the roots, first use the sum and product of roots; finding the roots individually is not necessary.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
By Vieta’s formulas, \(\alpha+\beta=12\) and \(\alpha\beta=35\). Therefore, \((\alpha-5)(\beta-5)=\alpha\beta-5(\alpha+\beta)+25=35-5(12)+25=0\). Hence, option A is correct. Exam tip: For expressions involving the roots, first use the sum and product of roots; finding the roots individually is not necessary.
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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