Suppose the quadratic equation \(ax^2+bx+c=0\) has two distinct real roots. Which condition definitely indicates that the roots have opposite signs?
Advertisement
Answer and explanation
Correct answer: \(\frac{c}{a}<0\)
By Vieta’s relation, the product of the roots is \(\alpha\beta=\frac{c}{a}\). If \(\frac{c}{a}<0\), one root is positive and the other is negative. For \(\frac{c}{a}>0\), real roots have the same sign. Exam tip: also check \(b^2-4ac>0\) for distinct real roots.
Frequently asked questions
What is the correct answer to this question?
\(\frac{c}{a}<0\)
Why is this the correct answer?
By Vieta’s relation, the product of the roots is \(\alpha\beta=\frac{c}{a}\). If \(\frac{c}{a}<0\), one root is positive and the other is negative. For \(\frac{c}{a}>0\), real roots have the same sign. Exam tip: also check \(b^2-4ac>0\) for distinct real roots.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
Advertisement