Choose the pair(s) of integers that can be substituted into the equation ax^2+8x+c=0 so that it has one real solution

Question

Choose the pair(s) of integers that can be substituted into the equation ax^2+8x+c=0 so that it has one real solution.

1. a=-2, c=-4
2. a=-1, c=-16
3. a=4, c=16
4. a=8, c=2

Answer 1

For one real solution b²-4ac must equal 0. Plugging in b

(8)²-4ac = 0 Add 4ac to both sides of the equation

64=4ac Divide both sides by 4

16=ac

So any 2 numbers that multiply together to give 16 will work.

1. a=-2, c=-4 (no)
2. a=-1, c=-16 (yes)
3. a=4, c=16 (no)
4. a=8, c=2 (yes)