What is the absolute difference between the roots of \(3x^2-14x+16=0\)?
Answer and explanation
Correct answer: \(\frac{2}{3}\)
Factoring gives \((3x-8)(x-2)=0\), so the roots are \(x=\frac{8}{3}\) and \(x=2\). Therefore, their absolute difference is \(\left|\frac{8}{3}-2\right|=\frac{2}{3}\). Exam tip: when the difference between roots is asked, use the larger root minus the smaller root unless an order is explicitly specified.
Frequently asked questions
What is the correct answer to this question?
\(\frac{2}{3}\)
Why is this the correct answer?
Factoring gives \((3x-8)(x-2)=0\), so the roots are \(x=\frac{8}{3}\) and \(x=2\). Therefore, their absolute difference is \(\left|\frac{8}{3}-2\right|=\frac{2}{3}\). Exam tip: when the difference between roots is asked, use the larger root minus the smaller root unless an order is explicitly specified.
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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