Question

question 12 of 23
use the discriminant to find possible solutions. do not solve.
$x^2 + 30x + 81 = 0$
select the correct response:
2 non - real solutions
2 real rational solutions
2 real irrational solutions
1 real rational solutions

Explanation:

Step1: Recall discriminant formula

For quadratic equation \(ax^2 + bx + c = 0\), discriminant \(D = b^2 - 4ac\).
Here, \(a = 1\), \(b = 30\), \(c = 81\).

Step2: Calculate discriminant

\(D = 30^2 - 4\times1\times81\)
\(= 900 - 324\)
\(= 576\)

Step3: Analyze discriminant

Since \(D = 576>0\) and \(576\) is a perfect square (\(\sqrt{576}=24\)), the quadratic has 2 real rational solutions.

Answer:

2 real rational solutions (corresponding to the option "2 real rational solutions")