The correct option is D. 0; One real root.
EXPLANATION
Given:
4x² + 12x + 9 = 0
From the above;
a=4 b=12 and c=9
Using the quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
Substitute the values.
[tex]x=\frac{-12\pm\sqrt[]{12^2-4(4)(9)}}{2\times4}[/tex][tex]=\frac{-12\pm\sqrt[]{144-144}}{8}[/tex][tex]=\frac{-12\pm\sqrt[]{0}}{8}[/tex]
Our interest is the value of b²-4ac.
If b²-4ac> 0, then the roots are real and unequal.
If b² - 4ac =0, then the roots are real and equal which implies there will be one root.
If b² - 4ac < 0, then the roots are complex.
In our case, the value of b²-4ac = 0, which implies we have just one real roots.
Therefore, the correct option is D. 0; One real root.
