What is the nature of the roots of the equation \(x^2+5x+7=0\)?
Answer and explanation
Correct answer: No real roots
For a quadratic equation \(ax^2+bx+c=0\), the discriminant is \(D=b^2-4ac\). Here, \(D=5^2-4(1)(7)=25-28=-3\), which is negative. Therefore, the equation has no real roots. Option A is incorrect because a negative discriminant cannot produce real roots. Exam tip: when \(D<0\), the quadratic has no real roots.
Frequently asked questions
What is the correct answer to this question?
No real roots
Why is this the correct answer?
For a quadratic equation \(ax^2+bx+c=0\), the discriminant is \(D=b^2-4ac\). Here, \(D=5^2-4(1)(7)=25-28=-3\), which is negative. Therefore, the equation has no real roots. Option A is incorrect because a negative discriminant cannot produce real roots. Exam tip: when \(D<0\), the quadratic has no real 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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