For which of the following values of c will there be 2 distinct real solutions to the equation 5x2+16x+ c = 0?

Explanation

The discriminant of a quadratic equation ax2 + bx + c = 0 is given by b2 - 4ac. For the equation to have two distinct real solutions, the discriminant must be greater than 0. Plugging the values into the equation with c = 3 gives a discriminant of 196, which is positive, thus allowing for two distinct real solutions. Other values for c either result in a negative discriminant (no real solutions) or do not yield distinct integer solutions even if positive.