For the quadratic equation \(x^2+(2h-1)x+h^2=0\) to have equal roots, what is the value of \(h\)?
Answer and explanation
Correct answer: \(h=\frac{1}{4}\)
A quadratic equation has equal roots when its discriminant is zero. Here, \(a=1\), \(b=2h-1\), and \(c=h^2\), so \(D=(2h-1)^2-4h^2=1-4h\). Setting \(D=0\) gives \(1-4h=0\), hence \(h=\frac{1}{4}\). Remember that equal roots always require a zero discriminant; for example, \(h=\frac{1}{2}\) gives \(D=-1\), so it is not correct.
Frequently asked questions
What is the correct answer to this question?
\(h=\frac{1}{4}\)
Why is this the correct answer?
A quadratic equation has equal roots when its discriminant is zero. Here, \(a=1\), \(b=2h-1\), and \(c=h^2\), so \(D=(2h-1)^2-4h^2=1-4h\). Setting \(D=0\) gives \(1-4h=0\), hence \(h=\frac{1}{4}\). Remember that equal roots always require a zero discriminant; for example, \(h=\frac{1}{2}\) gives \(D=-1\), so it is not correct.
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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