What is the nature of the roots of the equation \\(5x^2-30x+45=0\\)?
Answer and explanation
Correct answer: Two real and equal roots \\(D=0\\)
Here, \(a=5\), \(b=-30\), and \(c=45\). Therefore, the discriminant is \(D=b^2-4ac=(-30)^2-4(5)(45)=900-900=0\). Hence, the roots are real and equal. In fact, the equation can be written as \(5x^2-30x+45=5(x-3)^2=0\), giving the repeated root \(x=3\). Options B and D require \(D>0\), but here \(D=0\). Exam tip: For a quadratic equation, \(D=0\) always indicates two real and equal roots.
Frequently asked questions
What is the correct answer to this question?
Two real and equal roots \\(D=0\\)
Why is this the correct answer?
Here, \(a=5\), \(b=-30\), and \(c=45\). Therefore, the discriminant is \(D=b^2-4ac=(-30)^2-4(5)(45)=900-900=0\). Hence, the roots are real and equal. In fact, the equation can be written as \(5x^2-30x+45=5(x-3)^2=0\), giving the repeated root \(x=3\). Options B and D require \(D>0\), but here \(D=0\). Exam tip: For a quadratic equation, \(D=0\) always indicates two real and equal roots.
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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