If the discriminant of a quadratic equation is \(D=8m-24\), what condition on \(m\) is necessary for the equation to have real roots?
Answer and explanation
Correct answer: \(m\geq 3\)
A quadratic equation has real roots when its discriminant satisfies \(D\geq 0\). Thus, \(8m-24\geq 0\), which gives \(8m\geq 24\) and hence \(m\geq 3\). At \(m=3\), the roots are equal; for \(m>3\), the roots are distinct and real. Exam tip: when solving a discriminant inequality, check whether dividing by a negative quantity would reverse the inequality sign.
Frequently asked questions
What is the correct answer to this question?
\(m\geq 3\)
Why is this the correct answer?
A quadratic equation has real roots when its discriminant satisfies \(D\geq 0\). Thus, \(8m-24\geq 0\), which gives \(8m\geq 24\) and hence \(m\geq 3\). At \(m=3\), the roots are equal; for \(m>3\), the roots are distinct and real. Exam tip: when solving a discriminant inequality, check whether dividing by a negative quantity would reverse the inequality sign.
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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