For which of the following values of c will there be 2 distinct real solutions to the equation 5x2+16x+ c = 0?
Correct answer: A. 3
- A. 3
- B. 12
- C. 14
- D. 15
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.
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