Question

find the discriminant.
\\( 5z^2 - 3z = 0 \\)
what type of solutions does the equation have?
one real solution
two real solutions
two complex (non - real) solutions

Explanation:

Step1: Recall discriminant formula

For a quadratic equation \(az^2 + bz + c = 0\), the discriminant \(D\) is \(D = b^2 - 4ac\).
In the equation \(5z^2 - 3z = 0\), we have \(a = 5\), \(b = -3\), \(c = 0\).

Step2: Calculate the discriminant

Substitute \(a = 5\), \(b = -3\), \(c = 0\) into the formula:
\(D = (-3)^2 - 4\times5\times0\)
\(= 9 - 0\)
\(= 9\)

Step3: Determine the type of solutions

Since \(D = 9>0\), a quadratic equation with a positive discriminant has two distinct real solutions.

Answer:

Discriminant: \(9\); Type of solutions: two real solutions