Question

compute the discriminant. then determine the number and type of solutions of the given equation.\\(x^{2}-32x + 256 = 0\\)\\(\\)what is the discriminant?\\(\square\\) (simplify your answer.)

Explanation:

Step1: Recall discriminant formula

For quadratic $ax^2+bx+c=0$, discriminant $D=b^2-4ac$

Step2: Identify coefficients

$a=1$, $b=-32$, $c=256$

Step3: Calculate discriminant

$D=(-32)^2-4(1)(256)$
$D=1024-1024$
$D=0$

Step4: Analyze solution type

If $D=0$, one real repeated solution

Answer:

The discriminant is $0$. The equation has one real repeated solution.