For the quadratic equation \(x^2+2gx+g^2-6g+11=0\) to have equal roots, what should be the value of \(g\)?
Answer and explanation
Correct answer: \(g=\frac{11}{6}\)
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=1\), \(b=2g\), and \(c=g^2-6g+11\). Therefore, \(D=(2g)^2-4(g^2-6g+11)=24g-44\). Setting \(D=0\) gives \(24g-44=0\), so \(g=\frac{11}{6}\). Option B results from incorrectly reversing the numerator and denominator. In an exam, first apply the condition \(D=0\) for equal roots.
Frequently asked questions
What is the correct answer to this question?
\(g=\frac{11}{6}\)
Why is this the correct answer?
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=1\), \(b=2g\), and \(c=g^2-6g+11\). Therefore, \(D=(2g)^2-4(g^2-6g+11)=24g-44\). Setting \(D=0\) gives \(24g-44=0\), so \(g=\frac{11}{6}\). Option B results from incorrectly reversing the numerator and denominator. In an exam, first apply the condition \(D=0\) for equal roots.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
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