What is the difference between the larger and smaller roots of \(5x^2-22x+24=0\)?
Answer and explanation
Correct answer: \(\frac{2}{5}\)
Factoring gives \(5x^2-22x+24=(5x-12)(x-2)\). Therefore, the roots are \(\frac{12}{5}\) and \(2\). The difference between the larger and smaller roots is \(\frac{12}{5}-2=\frac{2}{5}\). The values \(\frac{12}{5}\) and \(2\) are the roots themselves, not their difference. In an exam, subtract the smaller root from the larger root when the difference between roots is asked.
Frequently asked questions
What is the correct answer to this question?
\(\frac{2}{5}\)
Why is this the correct answer?
Factoring gives \(5x^2-22x+24=(5x-12)(x-2)\). Therefore, the roots are \(\frac{12}{5}\) and \(2\). The difference between the larger and smaller roots is \(\frac{12}{5}-2=\frac{2}{5}\). The values \(\frac{12}{5}\) and \(2\) are the roots themselves, not their difference. In an exam, subtract the smaller root from the larger root when the difference between roots is asked.
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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