For the quadratic equation \(x^2-(a+6)x+6a=0\) to have equal roots, what is the value of \(a\)?
Answer and explanation
Correct answer: \(a=6\)
A quadratic equation has equal roots when its discriminant is zero. Here, \(D=[-(a+6)]^2-4(1)(6a)=(a+6)^2-24a=(a-6)^2\). Thus, \((a-6)^2=0\), giving \(a=6\). Exam tip: For equal-root questions, set the discriminant directly equal to zero; the other listed values produce distinct roots.
Frequently asked questions
What is the correct answer to this question?
\(a=6\)
Why is this the correct answer?
A quadratic equation has equal roots when its discriminant is zero. Here, \(D=[-(a+6)]^2-4(1)(6a)=(a+6)^2-24a=(a-6)^2\). Thus, \((a-6)^2=0\), giving \(a=6\). Exam tip: For equal-root questions, set the discriminant directly equal to zero; the other listed values produce distinct roots.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
