What is the sum of the roots of the equation \(3x^2-5x+2=0\)?
Answer and explanation
Correct answer: \(\frac{5}{3}\)
For a quadratic \(ax^2+bx+c=0\) the sum of roots equals \(-\frac{b}{a}\). Here \(a=3\) and \(b=-5\), so the sum is \(-\frac{-5}{3}=\frac{5}{3}\). The nearest distractor \(-\frac{5}{3}\) is a sign error; \(\frac{2}{3}\) is the product of the roots \(c/a\), not the sum. Exam tip: identify \(a,b,c\) first and then use \(-b/a\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{5}{3}\)
Why is this the correct answer?
For a quadratic \(ax^2+bx+c=0\) the sum of roots equals \(-\frac{b}{a}\). Here \(a=3\) and \(b=-5\), so the sum is \(-\frac{-5}{3}=\frac{5}{3}\). The nearest distractor \(-\frac{5}{3}\) is a sign error; \(\frac{2}{3}\) is the product of the roots \(c/a\), not the sum. Exam tip: identify \(a,b,c\) first and then use \(-b/a\).
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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