If \(\alpha\) and \(\beta\) are the roots of \(x^2-13x+36=0\), what is the value of \((\alpha+\beta)^2\)?
Answer and explanation
Correct answer: 169
For a quadratic equation \(ax^2+bx+c=0\), the sum of the roots is \(\alpha+\beta=-\frac{b}{a}\). Here, \(a=1\) and \(b=-13\), so \(\alpha+\beta=13\). Therefore, \((\alpha+\beta)^2=13^2=169\), making option A correct. Option B is the constant term, not the sum of the roots. Exam tip: Use Vieta’s formulas directly: the sum of roots is \(-\frac{b}{a}\) and their product is \(\frac{c}{a}\).
Frequently asked questions
What is the correct answer to this question?
169
Why is this the correct answer?
For a quadratic equation \(ax^2+bx+c=0\), the sum of the roots is \(\alpha+\beta=-\frac{b}{a}\). Here, \(a=1\) and \(b=-13\), so \(\alpha+\beta=13\). Therefore, \((\alpha+\beta)^2=13^2=169\), making option A correct. Option B is the constant term, not the sum of the roots. Exam tip: Use Vieta’s formulas directly: the sum of roots is \(-\frac{b}{a}\) and their product is \(\frac{c}{a}\).
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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