If one root of the equation \(x^2-(m+2)x+2m=0\) is \(2\), what is the other root?
Answer and explanation
Correct answer: \(m\)
For a quadratic equation \(ax^2+bx+c=0\), the product of its roots is \(\frac{c}{a}\). Here, the product of the two roots is \(2m\). Since one root is \(2\), the other root is \(\frac{2m}{2}=m\). As a check, the sum of the roots is \(m+2\), and \(2+m=m+2\), so the result is consistent. Exam tip: When one root is known, use either the product or the sum of roots, whichever gives the quicker calculation.
Frequently asked questions
What is the correct answer to this question?
\(m\)
Why is this the correct answer?
For a quadratic equation \(ax^2+bx+c=0\), the product of its roots is \(\frac{c}{a}\). Here, the product of the two roots is \(2m\). Since one root is \(2\), the other root is \(\frac{2m}{2}=m\). As a check, the sum of the roots is \(m+2\), and \(2+m=m+2\), so the result is consistent. Exam tip: When one root is known, use either the product or the sum of roots, whichever gives the quicker calculation.
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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