Question

question 14 of 23
1 point
use the discriminant to find possible solutions. do not solve.
$9x^2 - 24x = -16$
select the correct response:
2 non - real solutions
2 real rational solutions
2 real irrational solutions
1 real rational solution

Explanation:

Step1: Rewrite in standard form

The quadratic equation is \(9x^{2}-24x=-16\). Rewrite it as \(9x^{2}-24x + 16=0\). Here, \(a = 9\), \(b=-24\), \(c = 16\).

Step2: Calculate the discriminant

The discriminant formula is \(D=b^{2}-4ac\). Substitute \(a = 9\), \(b=-24\), \(c = 16\) into the formula:
\(D=(-24)^{2}-4\times9\times16\)
\(=576 - 576\)
\(=0\)

Step3: Analyze the discriminant

When the discriminant \(D = 0\), the quadratic equation has exactly one real solution. And since \(a\), \(b\), \(c\) are rational numbers, the solution is rational.

Answer:

1 real rational solution