Given:
There are given the equation:
[tex]x^2+6x+9=0[/tex]
Explanation:
To find the nature of the root, first, we need to find the value for the discriminant.
So,
From the formula of discriminant:
[tex]D=b^2-4ac[/tex]
According to the concept:
If,
[tex]\begin{gathered} D>0\rightarrow Real\text{ and unequal roots} \\ D=0\rightarrow Real\text{ and equal roots} \\ D<0\rightarrow No\text{ real roots} \end{gathered}[/tex]
Then,
To find the value of discriminant, put 1 for a, 6 for b, and 9 for c into the above formula:
[tex]\begin{gathered} \begin{equation*} D=b^2-4ac \end{equation*} \\ D=(6)^2-4(1)(9) \\ D=36-36 \\ D=0 \end{gathered}[/tex]
So,
According to the concept, we can say that there are real and equal roots.
Final answer:
hence, the correct option is A.
