If one root of the quadratic equation \(x^2-5x+q=0\) is 2, what is the value of \(q\)?
Answer and explanation
Correct answer: 6
Since 2 is a root, substitute \(x=2\) in the equation: \(2^2-5(2)+q=0\), giving \(4-10+q=0\) and hence \(q=6\). Alternatively, the sum of the roots is 5, so the other root is 3 and their product is \(q=2\times3=6\). Exam tip: for \(x^2+bx+c=0\), the product of the roots is \(c\); 10 is related to neither the required constant term nor the correct substitution result.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
Since 2 is a root, substitute \(x=2\) in the equation: \(2^2-5(2)+q=0\), giving \(4-10+q=0\) and hence \(q=6\). Alternatively, the sum of the roots is 5, so the other root is 3 and their product is \(q=2\times3=6\). Exam tip: for \(x^2+bx+c=0\), the product of the roots is \(c\); 10 is related to neither the required constant term nor the correct substitution result.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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