For the quadratic equation \(ax^2+bx+c=0\), under which condition will the roots be real?
Answer and explanation
Correct answer: \(D\ge 0\)
The discriminant \(D=b^2-4ac\) determines the nature of roots. If \(D>0\) there are two distinct real roots, if \(D=0\) there is one repeated real root; hence real roots occur exactly when \(D\ge 0\). Option A is incorrect because \(D<0\) gives complex (non-real) roots. Option C is just a specific value and not a general condition. Option D is incorrect because \(a=0\) makes the equation linear, not quadratic. Exam tip: compute \(D=b^2-4ac\) first to decide root nature quickly.
Frequently asked questions
What is the correct answer to this question?
\(D\ge 0\)
Why is this the correct answer?
The discriminant \(D=b^2-4ac\) determines the nature of roots. If \(D>0\) there are two distinct real roots, if \(D=0\) there is one repeated real root; hence real roots occur exactly when \(D\ge 0\). Option A is incorrect because \(D<0\) gives complex (non-real) roots. Option C is just a specific value and not a general condition. Option D is incorrect because \(a=0\) makes the equation linear, not quadratic. Exam tip: compute \(D=b^2-4ac\) first to decide root nature quickly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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