If \(a\ne0\) in the quadratic equation \(ax^2+bx+c=0\), and its roots are real and equal, which of the following conditions is correct?
Answer and explanation
Correct answer: \(b^2=4ac\)
The nature of the roots is determined by the discriminant \(\Delta=b^2-4ac\). Real and equal roots occur only when \(\Delta=0\), which gives \(b^2=4ac\). If \(b^2>4ac\), the roots are real and distinct; if \(b^2<4ac\), they are non-real. Exam tip: for equal roots, immediately set the discriminant equal to zero.
Frequently asked questions
What is the correct answer to this question?
\(b^2=4ac\)
Why is this the correct answer?
The nature of the roots is determined by the discriminant \(\Delta=b^2-4ac\). Real and equal roots occur only when \(\Delta=0\), which gives \(b^2=4ac\). If \(b^2>4ac\), the roots are real and distinct; if \(b^2<4ac\), they are non-real. Exam tip: for equal roots, immediately set the discriminant equal to zero.
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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