If the discriminant of a quadratic equation is \(D=(m-8)^2\), what must be the value of \(m\) for the equation to have equal roots?
Answer and explanation
Correct answer: \(m=8\)
A quadratic equation has equal roots only when its discriminant is \(D=0\). Therefore, \((m-8)^2=0\), which gives \(m-8=0\) and hence \(m=8\). Option D is incorrect because \((m-8)^2\) is not zero for every real value of \(m\). Exam tip: For equal-root questions, begin by setting the discriminant equal to zero.
Frequently asked questions
What is the correct answer to this question?
\(m=8\)
Why is this the correct answer?
A quadratic equation has equal roots only when its discriminant is \(D=0\). Therefore, \((m-8)^2=0\), which gives \(m-8=0\) and hence \(m=8\). Option D is incorrect because \((m-8)^2\) is not zero for every real value of \(m\). Exam tip: For equal-root questions, begin by setting the discriminant equal to zero.
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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