Question

I will give medal!!!! Help please!
create three functions in standard form.
f(x), with two real rational solutions.
g(x), with two real irrational solutions.
h(x), with two complex solutions.

Answer 1

for a polynomial: ax^2 + bx + c = 0

the two solutions/roots would be:

\[x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }\]

the parameter which defines what the solutions will be like is:\[\sqrt{b^2 - 4ac}\]

if (the discriminant): b^2 - 4ac < 0, the number under the root is negative, which leads to "complex" solutions [containing i = sqrt(-1)]

if sqrt(b^2 - 4ac) is rational. so are the two x values.
if sqrt(b^2 - 4ac) is irrational. so are the two x values.