What is the nature of the roots of the equation \(12x^2-12x+3=0\)?
Answer and explanation
Correct answer: Two real and equal roots \((D=0)\)
Here, \(a=12\), \(b=-12\), and \(c=3\). Therefore, the discriminant is \(D=b^2-4ac=(-12)^2-4(12)(3)=144-144=0\). When \(D=0\), the roots are real and equal. In fact, the equation can be written as \(3(2x-1)^2=0\), giving the repeated root \(x=\frac{1}{2}\). Option B is incorrect because \(D>0\) gives two distinct real roots. Exam tip: For a quadratic equation, \(D=0\) always indicates equal real 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, \(a=12\), \(b=-12\), and \(c=3\). Therefore, the discriminant is \(D=b^2-4ac=(-12)^2-4(12)(3)=144-144=0\). When \(D=0\), the roots are real and equal. In fact, the equation can be written as \(3(2x-1)^2=0\), giving the repeated root \(x=\frac{1}{2}\). Option B is incorrect because \(D>0\) gives two distinct real roots. Exam tip: For a quadratic equation, \(D=0\) always indicates equal real 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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