If the product of two real roots is positive and their sum is positive, how will both roots be?
Answer and explanation
Correct answer: Both positive
Let the two real roots be α and β. Their product αβ is positive, so the roots must have the same sign: both positive or both negative. Their sum α + β is also positive. If both roots were negative, their sum would necessarily be negative, so that possibility is ruled out. Therefore both roots are positive. Option C would give a negative product, while option D would make the product zero, not positive. This conclusion uses the sign relationships between the sum and product of two real numbers, and it does not require calculating the roots individually.
Frequently asked questions
What is the correct answer to this question?
Both positive
Why is this the correct answer?
Let the two real roots be α and β. Their product αβ is positive, so the roots must have the same sign: both positive or both negative. Their sum α + β is also positive. If both roots were negative, their sum would necessarily be negative, so that possibility is ruled out. Therefore both roots are positive. Option C would give a negative product, while option D would make the product zero, not positive. This conclusion uses the sign relationships between the sum and product of two real numbers, and it does not require calculating the roots individually.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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