Question

Find the nature of the roots of x2 + 6x + 9 = 0.

Answer 1

Given:

There are given the equation:

`x^2+6x+9=0`

Step-by-step explanation:

To find the nature of the root, first, we need to find the value for the discriminant.

So,

From the formula of discriminant:

`D=b^2-4ac`

According to the concept:

If,

`\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}`

Then,

To find the value of discriminant, put 1 for a, 6 for b, and 9 for c into the above formula:

`\begin{gathered} \begin{equation*} D=b^2-4ac \end{equation*} \\ D=(6)^2-4(1)(9) \\ D=36-36 \\ D=0 \end{gathered}`

So,

According to the concept, we can say that there are real and equal roots.

Final answer:

hence, the correct option is A.