Algebra II Word Problem

Question

Find ONE possible pair of integer values of a and c so that the following equation has the given solutions.

equation is: ax^2 -8x +c = 0

give two possible imaginary solutions for a and c

Answer 1

so for this we will use the discriminant to find what values of a and c give imaginary roots:

b²-4ac; 64-4ac<0, 64<4ac, 16<ac so we can say a=1 and c=17

x²-8x+17=0

x=(8±sqrt(64-68))/2, x=(8±sqrt(-4))/2, x=(8±2i)/2, x=4±i