The equation \(x^2+8x+k=0\) has no real roots. What is the correct condition on \(k\)?
Answer and explanation
Correct answer: \(k>16\)
A quadratic equation has no real roots only when its discriminant \(D=b^2-4ac\) is negative. Here, \(a=1, b=8, c=k\), so \(D=8^2-4(1)(k)=64-4k\). Thus, \(64-4k<0\), which gives \(k>16\). Note that \(k=16\) makes the discriminant zero and produces one repeated real root, so it is not correct.
Frequently asked questions
What is the correct answer to this question?
\(k>16\)
Why is this the correct answer?
A quadratic equation has no real roots only when its discriminant \(D=b^2-4ac\) is negative. Here, \(a=1, b=8, c=k\), so \(D=8^2-4(1)(k)=64-4k\). Thus, \(64-4k<0\), which gives \(k>16\). Note that \(k=16\) makes the discriminant zero and produces one repeated real root, so it is not correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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