If the discriminant of the quadratic equation \\(ax^2+bx+c=0\\) is \\(D=b^2-4ac\\), what is the nature of its roots when \\(D>0\\)?
Answer and explanation
Correct answer: Two real and distinct roots
The roots of a quadratic equation are \\(\frac{-b\pm\sqrt{D}}{2a}\\). When \\(D>0\\), \\(\sqrt{D}\\) is a positive real number, so the plus and minus forms give two real and distinct roots. For comparison, \\(D=0\\) gives equal roots, while \\(D<0\\) gives no real roots. In an exam, first calculate or determine the sign of the discriminant \\(D=b^2-4ac\\).
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What is the correct answer to this question?
Two real and distinct roots
Why is this the correct answer?
The roots of a quadratic equation are \\(\frac{-b\pm\sqrt{D}}{2a}\\). When \\(D>0\\), \\(\sqrt{D}\\) is a positive real number, so the plus and minus forms give two real and distinct roots. For comparison, \\(D=0\\) gives equal roots, while \\(D<0\\) gives no real roots. In an exam, first calculate or determine the sign of the discriminant \\(D=b^2-4ac\\).
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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