If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^2-6x+1=0\), what is the value of \(\alpha+\beta\)?
Answer and explanation
Correct answer: \(3\)
For a quadratic equation \(ax^2+bx+c=0\), the sum of the roots is \(\alpha+\beta=-\frac{b}{a}\). Here, \(a=2\) and \(b=-6\), so \(\alpha+\beta=-\frac{-6}{2}=3\). Option B results from mishandling the negative sign of \(b\). Exam tip: identify the coefficients carefully before applying \(-b/a\).
Frequently asked questions
What is the correct answer to this question?
\(3\)
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, \(a=2\) and \(b=-6\), so \(\alpha+\beta=-\frac{-6}{2}=3\). Option B results from mishandling the negative sign of \(b\). Exam tip: identify the coefficients carefully before applying \(-b/a\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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