Question

find the discriminant.
$2u^2 - 3u + 6 = 0$
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 \(au^2 + bu + c = 0\), the discriminant \(D\) is given by \(D = b^2 - 4ac\).
Here, \(a = 2\), \(b = -3\), \(c = 6\).

Step2: Calculate the discriminant

Substitute the values into the formula:
\(D = (-3)^2 - 4\times2\times6\)
\(= 9 - 48\)
\(= -39\)

Step3: Determine the type of solutions

• If \(D > 0\), two distinct real solutions.
• If \(D = 0\), one real solution.
• If \(D < 0\), two complex (non - real) solutions.

Since \(D=-39 < 0\), the equation has two complex (non - real) solutions.

Answer:

The discriminant is \(-39\). The equation has two complex (non - real) solutions.