For the quadratic equation ax^2+bx+c=0 with discriminant D = b^2 - 4ac, in which condition are there no real roots?
Answer and explanation
Correct answer: \(D<0\)
The sign of the discriminant D determines the nature of the roots. When \(D<0\) the quantity \(\sqrt{D}\) is not real, so the roots are complex conjugates and there are no real roots. If \(D>0\) there are two distinct real roots, and if \(D=0\) there is one repeated real root; thus those options are incorrect. Exam tip: compute \(b^2-4ac\) quickly — if it is negative you can immediately conclude there are no real roots.
Frequently asked questions
What is the correct answer to this question?
\(D<0\)
Why is this the correct answer?
The sign of the discriminant D determines the nature of the roots. When \(D<0\) the quantity \(\sqrt{D}\) is not real, so the roots are complex conjugates and there are no real roots. If \(D>0\) there are two distinct real roots, and if \(D=0\) there is one repeated real root; thus those options are incorrect. Exam tip: compute \(b^2-4ac\) quickly — if it is negative you can immediately conclude there are no real roots.
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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