What is the nature of the roots of the quadratic equation \(36x^2-60kx+25k^2=0\)?
Answer and explanation
Correct answer: Two equal real roots
The quadratic is a perfect square: \((6x-5k)^2=0\). Alternatively compute the discriminant: \(\Delta=b^2-4ac=(-60k)^2-4\cdot36\cdot25k^2=3600k^2-3600k^2=0\). A zero discriminant means the two roots are equal and real (root \(x=5k/6\)). Option B is wrong because that requires \(\Delta>0\); option C is wrong because that requires \(\Delta<0\); option D is wrong because the nature does not depend on a special value of k for real k — it is always equal roots. Exam tip: check the discriminant first or try factoring into a perfect square to save time.
Frequently asked questions
What is the correct answer to this question?
Two equal real roots
Why is this the correct answer?
The quadratic is a perfect square: \((6x-5k)^2=0\). Alternatively compute the discriminant: \(\Delta=b^2-4ac=(-60k)^2-4\cdot36\cdot25k^2=3600k^2-3600k^2=0\). A zero discriminant means the two roots are equal and real (root \(x=5k/6\)). Option B is wrong because that requires \(\Delta>0\); option C is wrong because that requires \(\Delta<0\); option D is wrong because the nature does not depend on a special value of k for real k — it is always equal roots. Exam tip: check the discriminant first or try factoring into a perfect square to save time.
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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