If the discriminant of a quadratic equation is \(D=12n-36\), what condition on \(n\) is necessary for the equation to have two real and distinct roots?
Answer and explanation
Correct answer: \(n>3\)
A quadratic equation has two real and distinct roots only when its discriminant satisfies \(D>0\). Therefore, \(12n-36>0\), which gives \(12n>36\) and hence \(n>3\). At \(n=3\), \(D=0\), so the roots are real but equal. Exam tip: remember \(D>0\) for two real and distinct roots.
Frequently asked questions
What is the correct answer to this question?
\(n>3\)
Why is this the correct answer?
A quadratic equation has two real and distinct roots only when its discriminant satisfies \(D>0\). Therefore, \(12n-36>0\), which gives \(12n>36\) and hence \(n>3\). At \(n=3\), \(D=0\), so the roots are real but equal. Exam tip: remember \(D>0\) for two real and distinct roots.
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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