If the quadratic equation \(2x^2+\lambda x+8=0\) has equal roots, what can be the values of \(\lambda\)?
Answer and explanation
Correct answer: \(\lambda=\pm 8\)
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=2\), \(b=\lambda\), and \(c=8\), so \(D=\lambda^2-4(2)(8)=\lambda^2-64\). Thus, \(\lambda^2-64=0\), giving \(\lambda=\pm8\). Option B may result from incorrectly calculating \(4ac\). Exam tip: For equal roots of a quadratic equation, set the discriminant directly equal to zero.
Frequently asked questions
What is the correct answer to this question?
\(\lambda=\pm 8\)
Why is this the correct answer?
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=2\), \(b=\lambda\), and \(c=8\), so \(D=\lambda^2-4(2)(8)=\lambda^2-64\). Thus, \(\lambda^2-64=0\), giving \(\lambda=\pm8\). Option B may result from incorrectly calculating \(4ac\). Exam tip: For equal roots of a quadratic equation, set the discriminant directly equal to zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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