What is the nature of the roots of the quadratic equation \(16x^2-24kx+9k^2=0\)?
Answer and explanation
Correct answer: Two equal real roots
The equation can be written as \((4x-3k)^2=0\). Hence \(4x-3k=0\), giving the repeated root \(x=\frac{3k}{4}\). Equivalently, the discriminant is \(D=b^2-4ac=0\), which confirms that the roots are equal and real. Exam tip: for a quadratic equation, \(D=0\) indicates two equal real roots.
Frequently asked questions
What is the correct answer to this question?
Two equal real roots
Why is this the correct answer?
The equation can be written as \((4x-3k)^2=0\). Hence \(4x-3k=0\), giving the repeated root \(x=\frac{3k}{4}\). Equivalently, the discriminant is \(D=b^2-4ac=0\), which confirms that the roots are equal and real. Exam tip: for a quadratic equation, \(D=0\) indicates two equal real roots.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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