Question

Is the equations of quadratic number pattern will always have real roots

Answer 1

No, not at all.

The general quadratic equation is

                         Ax² + Bx + C = 0 .

The roots are real only if  (B² - 4AC) is not negative.

That means if you graph it, it touches or crosses the x-axis.

If the graph is up in the air and never touches the x-axis,
then it has no real roots.