If the quadratic equation \(x^2-2hx+h^2+8h=0\) has equal roots, what is the value of \(h\)?
Answer and explanation
Correct answer: \(h=0\)
For equal roots, the discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=1\), \(b=-2h\), and \(c=h^2+8h\). Thus, \(D=(-2h)^2-4(1)(h^2+8h)=-32h\). Setting \(-32h=0\) gives \(h=0\). Indeed, for this value the equation becomes \(x^2=0\), whose two roots are both \(0\). Exam tip: For equal roots of a quadratic equation, immediately use the condition \(D=0\).
Frequently asked questions
What is the correct answer to this question?
\(h=0\)
Why is this the correct answer?
For equal roots, the discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=1\), \(b=-2h\), and \(c=h^2+8h\). Thus, \(D=(-2h)^2-4(1)(h^2+8h)=-32h\). Setting \(-32h=0\) gives \(h=0\). Indeed, for this value the equation becomes \(x^2=0\), whose two roots are both \(0\). Exam tip: For equal roots of a quadratic equation, immediately use the condition \(D=0\).
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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