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