If \(x=-2\) is a root of the equation \(x^2+(3k+1)x+2k=0\), what is the value of \(k\)?
Answer and explanation
Correct answer: \(\frac{1}{2}\)
Since \(x=-2\) is a root, substitute it into the equation: \((-2)^2+(3k+1)(-2)+2k=0\). This gives \(4-6k-2+2k=0\), so \(2-4k=0\) and hence \(k=\frac{1}{2}\). The nearby distractor \(k=-\frac{1}{2}\) does not make the equation equal to zero. Exam tip: when a root is given, substitute it directly into the polynomial equation.
Frequently asked questions
What is the correct answer to this question?
\(\frac{1}{2}\)
Why is this the correct answer?
Since \(x=-2\) is a root, substitute it into the equation: \((-2)^2+(3k+1)(-2)+2k=0\). This gives \(4-6k-2+2k=0\), so \(2-4k=0\) and hence \(k=\frac{1}{2}\). The nearby distractor \(k=-\frac{1}{2}\) does not make the equation equal to zero. Exam tip: when a root is given, substitute it directly into the polynomial equation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
