If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2+2x-8=0\), what is the value of \((\alpha+\beta)^2\)?
Answer and explanation
Correct answer: 4
By Vieta’s formula, the sum of the roots of \(ax^2+bx+c=0\) is \(\alpha+\beta=-\frac{b}{a}\). Here, \(a=1\) and \(b=2\), so \(\alpha+\beta=-2\). Therefore, \((\alpha+\beta)^2=(-2)^2=4\). Exam tip: square the complete sum, including its sign; the negative sign disappears only after squaring.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
By Vieta’s formula, the sum of the roots of \(ax^2+bx+c=0\) is \(\alpha+\beta=-\frac{b}{a}\). Here, \(a=1\) and \(b=2\), so \(\alpha+\beta=-2\). Therefore, \((\alpha+\beta)^2=(-2)^2=4\). Exam tip: square the complete sum, including its sign; the negative sign disappears only after squaring.
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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