If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-15x+44=0\), what is the value of \((\alpha+\beta)^2\)?
Answer and explanation
Correct answer: 225
By Vieta’s formula, the sum of the roots of \(ax^2+bx+c=0\) is \(-\frac{b}{a}\). Here, \(a=1\) and \(b=-15\), so \(\alpha+\beta=-\frac{-15}{1}=15\). Therefore, \((\alpha+\beta)^2=15^2=225\). The value 44 is the product \(\alpha\beta\), not the sum of the roots. Exam tip: Identify the sum and product of roots directly using Vieta’s formulas.
Frequently asked questions
What is the correct answer to this question?
225
Why is this the correct answer?
By Vieta’s formula, the sum of the roots of \(ax^2+bx+c=0\) is \(-\frac{b}{a}\). Here, \(a=1\) and \(b=-15\), so \(\alpha+\beta=-\frac{-15}{1}=15\). Therefore, \((\alpha+\beta)^2=15^2=225\). The value 44 is the product \(\alpha\beta\), not the sum of the roots. Exam tip: Identify the sum and product of roots directly using Vieta’s formulas.
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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