quadratic equation?

Question

Find the values of​ a, b, and c for which the quadratic equation ax^2+bx+c=0 has the solutions 10i and −10i.​(Hint: Use the​ zero-product property in​ reverse.)

Answer 1

ax² + bx + c = a(x - 10i)(x + 10i) = a[x² - (10i)²]

ax² + bx + c = a(x² + 100) = ax² + 100a

a = any real nonzero number

b = 0

c = 100a