Question

find the discriminant.
$5z^{2}-5z = 0$
how many real solutions does the equation have?
no real solutions
one real solution
two real solutions

Explanation:

Step1: Identify quadratic coefficients

For $5z^2 - 5z = 0$, $a=5$, $b=-5$, $c=0$

Step2: Apply discriminant formula

Discriminant $D = b^2 - 4ac$
$D = (-5)^2 - 4(5)(0)$

Step3: Calculate discriminant value

$D = 25 - 0 = 25$

Step4: Determine real solutions

Since $D>0$, there are two real solutions.

Answer:

Discriminant: $25$
Number of real solutions: two real solutions