Question

Which of the statements about the following quadratic equation is true?
T

Answer 1

The correct option is D. 0; One real root.

Step-by-step explanation

Given:

4x² + 12x + 9 = 0

From the above;

a=4 b=12 and c=9

Using the quadratic formula

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

Substitute the values.

`x=\frac{-12\pm\sqrt[]{12^2-4(4)(9)}}{2*4}`
`=\frac{-12\pm\sqrt[]{144-144}}{8}`
`=\frac{-12\pm\sqrt[]{0}}{8}`

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.