Sign of Coefficient in Quadratic Equation

Hard Problem Solving Algebra

Consider the quadratic equation $$ax^2 + bx + c = 0$$ with the following conditions:

1. The roots of the equation are real and distinct.

2. The relationship between the coefficients is given by: $$b^2 - 4ac > 0$$.

If we know that the coefficients satisfy the equation $$4a + 5b + 6c = 0$$, what can we determine about the sign of $$a$$?

$$a$$ must be positive.

$$a$$ must be negative.

$$a$$ can be either positive or negative.

$$a$$ is equal to zero.

Submitted4.1K

Correct3.6K

% Correct86%