Question

compute the discriminant. then determine the number and type of solutions of the given equation
$x^2 - 24x + 144 = 0$
...
what is the discriminant?
\boxed{} (simplify your answer.)

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, here $a=1$, $b=-24$, $c=144$.

Step2: Apply discriminant formula

Discriminant $D = b^2-4ac$
$D = (-24)^2 - 4(1)(144)$

Step3: Calculate each term

$(-24)^2=576$, $4(1)(144)=576$

Step4: Compute final discriminant

$D = 576 - 576$

Answer:

0

Additionally, since the discriminant is 0, the quadratic equation has one real repeated rational solution.