What is the nature of the roots of the equation \(3x^2-12=0\)?
Answer and explanation
Correct answer: Two real, rational and distinct roots
For the equation \(3x^2-12=0\), \(a=3\), \(b=0\), and \(c=-12\). Thus, the discriminant is \(D=b^2-4ac=0-4(3)(-12)=144\). Since \(D>0\), the roots are real and distinct; because \(\sqrt{D}=12\) is an integer, both roots are rational. In fact, the roots are \(x=2\) and \(x=-2\). Exam tip: If \(D>0\) and is a perfect square, the roots are real, rational, and distinct.
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What is the correct answer to this question?
Two real, rational and distinct roots
Why is this the correct answer?
For the equation \(3x^2-12=0\), \(a=3\), \(b=0\), and \(c=-12\). Thus, the discriminant is \(D=b^2-4ac=0-4(3)(-12)=144\). Since \(D>0\), the roots are real and distinct; because \(\sqrt{D}=12\) is an integer, both roots are rational. In fact, the roots are \(x=2\) and \(x=-2\). Exam tip: If \(D>0\) and is a perfect square, the roots are real, rational, and distinct.
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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