If the discriminant of a quadratic equation is (D=(m-5)^2), which value of (m) is required for its roots to be equal?
Answer and explanation
Correct answer: \(m=5\)
A quadratic equation has equal roots when its discriminant is \(D=0\). Thus, \((m-5)^2=0\), which gives \(m-5=0\) and hence \(m=5\). If \(m=-5\), the discriminant is \((-10)^2=100\), so the roots are not equal. Exam tip: The square of a real number is zero only when the number itself is zero.
Frequently asked questions
What is the correct answer to this question?
\(m=5\)
Why is this the correct answer?
A quadratic equation has equal roots when its discriminant is \(D=0\). Thus, \((m-5)^2=0\), which gives \(m-5=0\) and hence \(m=5\). If \(m=-5\), the discriminant is \((-10)^2=100\), so the roots are not equal. Exam tip: The square of a real number is zero only when the number itself is zero.
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.
