For the quadratic equation \(ax^2+bx+c=0\) with real coefficients, where \(a\ne0\), if \(\frac{c}{a}<0\), which statement about its roots is correct?
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Answer and explanation
Correct answer: Both roots are real and have opposite signs
By Vieta’s relation, the product of the roots is \(\frac{c}{a}\). A negative product gives opposite signs. Also, \(ac<0\) makes \(b^2-4ac>0\), so both roots are real. Exam tip: use the sign of the product to identify root signs.
Frequently asked questions
What is the correct answer to this question?
Both roots are real and have opposite signs
Why is this the correct answer?
By Vieta’s relation, the product of the roots is \(\frac{c}{a}\). A negative product gives opposite signs. Also, \(ac<0\) makes \(b^2-4ac>0\), so both roots are real. Exam tip: use the sign of the product to identify root signs.
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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