If \(\alpha\) and \(\beta\) are the roots of the equation \(3x^2-12x+5=0\), what is the value of \(\alpha+\beta\)?
Answer and explanation
Correct answer: 4
For a quadratic equation \(ax^2+bx+c=0\), the sum of the roots is \(\alpha+\beta=-\frac{b}{a}\). Here, \(a=3\) and \(b=-12\), so \(\alpha+\beta=-\frac{-12}{3}=4\). Option B has the wrong sign, while \(\frac{5}{3}\) and \(-\frac{5}{3}\) are related to the product of the roots, not their sum. Exam tip: Always check the sign of \(b\) before applying the formula.
Frequently asked questions
What is the correct answer to this question?
4
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, \(a=3\) and \(b=-12\), so \(\alpha+\beta=-\frac{-12}{3}=4\). Option B has the wrong sign, while \(\frac{5}{3}\) and \(-\frac{5}{3}\) are related to the product of the roots, not their sum. Exam tip: Always check the sign of \(b\) before applying the formula.
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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