What is the repeated root of the equation \(4x^2-20x+25=0\)?
Answer and explanation
Correct answer: \(x=\frac{5}{2}\)
Here, \(a=4, b=-20, c=25\). The discriminant is \(D=b^2-4ac=(-20)^2-4(4)(25)=0\), so the two roots are equal. Factoring gives \((2x-5)^2=0\), hence \(2x-5=0\) and the repeated root is \(x=\frac{5}{2}\). Exam tip: When \(D=0\), the equal root can also be found directly using \(x=\frac{-b}{2a}\).
Frequently asked questions
What is the correct answer to this question?
\(x=\frac{5}{2}\)
Why is this the correct answer?
Here, \(a=4, b=-20, c=25\). The discriminant is \(D=b^2-4ac=(-20)^2-4(4)(25)=0\), so the two roots are equal. Factoring gives \((2x-5)^2=0\), hence \(2x-5=0\) and the repeated root is \(x=\frac{5}{2}\). Exam tip: When \(D=0\), the equal root can also be found directly using \(x=\frac{-b}{2a}\).
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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