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For positive values of a, b and c, consider the quadratic equation ax² + bx + c = 0. What can be said about its two roots?

1. Both roots are real and less than zero
2. Both roots have negative real parts
3. Both roots are rational
4. None of the above

Correct answer: Both roots have negative real parts

Solution

The roots of the quadratic equation can be determined using the quadratic formula, and since the coefficients a, b, and c are all positive, the sum of the roots (given by -b/a) is negative, indicating that both roots must have negative real parts.

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