If the discriminant of a quadratic equation is \(D=(u+1)(u-5)\), which interval of \(u\) results in no real roots?
Answer and explanation
Correct answer: \(-1<u<5\)
A quadratic equation has no real roots when its discriminant satisfies \(D<0\). Therefore, \((u+1)(u-5)<0\). The zeros of the two factors are \(-1\) and \(5\), and their product is negative between these values, giving \(-1<u<5\). At the endpoints, \(D=0\), so the equation has two equal real roots. Exam tip: First write the required discriminant condition, then check the sign of the product between its critical values.
Frequently asked questions
What is the correct answer to this question?
\(-1<u<5\)
Why is this the correct answer?
A quadratic equation has no real roots when its discriminant satisfies \(D<0\). Therefore, \((u+1)(u-5)<0\). The zeros of the two factors are \(-1\) and \(5\), and their product is negative between these values, giving \(-1<u<5\). At the endpoints, \(D=0\), so the equation has two equal real roots. Exam tip: First write the required discriminant condition, then check the sign of the product between its critical values.
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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