What is the difference between the roots of the equation \(2x^2-9x+10=0\), taking the larger root minus the smaller root?
Answer and explanation
Correct answer: \(\frac{1}{2}\)
Here, the discriminant is \(D=b^2-4ac=(-9)^2-4(2)(10)=81-80=1\). The difference between the roots is \(\frac{\sqrt{D}}{|a|}\), so it equals \(\frac{\sqrt{1}}{2}=\frac{1}{2}\). Alternatively, \(2x^2-9x+10=(2x-5)(x-2)\), giving roots \(\frac{5}{2}\) and \(2\), whose difference is \(\frac{1}{2}\). Exam tip: use \(\frac{\sqrt{D}}{|a|}\) when only the difference between roots is required.
Frequently asked questions
What is the correct answer to this question?
\(\frac{1}{2}\)
Why is this the correct answer?
Here, the discriminant is \(D=b^2-4ac=(-9)^2-4(2)(10)=81-80=1\). The difference between the roots is \(\frac{\sqrt{D}}{|a|}\), so it equals \(\frac{\sqrt{1}}{2}=\frac{1}{2}\). Alternatively, \(2x^2-9x+10=(2x-5)(x-2)\), giving roots \(\frac{5}{2}\) and \(2\), whose difference is \(\frac{1}{2}\). Exam tip: use \(\frac{\sqrt{D}}{|a|}\) when only the difference between roots is required.
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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