Which conclusion about the nature of the roots of the equation \(x^2+4x+8=0\) is correct?
Answer and explanation
Correct answer: There are no real roots
Here, \(a=1\), \(b=4\), and \(c=8\). The discriminant is \(D=b^2-4ac=4^2-4(1)(8)=16-32=-16<0\). Therefore, the equation has no real roots. The roots would be real and equal only if \(D=0\). In an exam, first check the sign of the discriminant to determine the nature of the roots.
Frequently asked questions
What is the correct answer to this question?
There are no real roots
Why is this the correct answer?
Here, \(a=1\), \(b=4\), and \(c=8\). The discriminant is \(D=b^2-4ac=4^2-4(1)(8)=16-32=-16<0\). Therefore, the equation has no real roots. The roots would be real and equal only if \(D=0\). In an exam, first check the sign of the discriminant to determine the nature of the 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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