Quadratic equation and nature of roots

What can you say about the roots of the following quadratic equation?

[math]x^2+4x+6=0[/math]

The roots are real The roots are not equal The roots are not real The roots are irrational The roots are rational The roots are equal

[math]x^2+4x+4=0[/math]

The roots are real The roots are irrational The two roots are unequal The roots are rational The two roots are equal The roots are not real

[math]x^2+4x-5=0[/math]

The roots are not real The two roots are equal The roots are rational The roots are real The roots are irrational The two roots are unequal

[math]x^2+4x-2=0[/math]

The roots are rational The two roots are unequal The roots are not real The roots are real The roots are irrational The two roots are equal

Can you construct a quadratic equation with integral coefficient whose roots are irrational and repeated?

Information: Quadratic equation and nature of roots