If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-9x+14=0\), what is the value of \((\alpha+\beta)^2\)?
Answer and explanation
Correct answer: 81
For a quadratic equation \(ax^2+bx+c=0\), the sum of the roots is \(\alpha+\beta=-\frac{b}{a}\). Here, \(a=1\) and \(b=-9\), so \(\alpha+\beta=9\). Therefore, \((\alpha+eta)^2=9^2=81\). The value 14 is the product \(\alpha\beta\), not the sum of the roots. Exam tip: remember that the sum of roots is \(-b/a\), while their product is \(c/a\).
Frequently asked questions
What is the correct answer to this question?
81
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 \(b=-9\), so \(\alpha+\beta=9\). Therefore, \((\alpha+eta)^2=9^2=81\). The value 14 is the product \(\alpha\beta\), not the sum of the roots. Exam tip: remember that the sum of roots is \(-b/a\), while their product is \(c/a\).
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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