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If \(x=-1\) is a root of the quadratic equation \(x^2+(4k-1)x+3k=0\), what is the value of \(k\)?
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Answer and explanation
Correct answer: 2
Since \(x=-1\) is a root, substitute it into the equation: \((-1)^2+(4k-1)(-1)+3k=0\). This gives \(1-4k+1+3k=0\), or \(2-k=0\), so \(k=2\). Exam tip: When a root is given, substitute it directly into the polynomial to form an equation in the parameter.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
Since \(x=-1\) is a root, substitute it into the equation: \((-1)^2+(4k-1)(-1)+3k=0\). This gives \(1-4k+1+3k=0\), or \(2-k=0\), so \(k=2\). Exam tip: When a root is given, substitute it directly into the polynomial to form an equation in the parameter.
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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