Question

find the discriminant.
2u² + 4u + 2 = 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 $\Delta=b^{2}-4ac$.

Step2: Identify coefficients

In the equation $2u^{2}+4u + 2 = 0$, $a = 2$, $b = 4$, $c = 2$.

Step3: Calculate discriminant

$\Delta=(4)^{2}-4\times2\times2$
$=16 - 16$
$=0$

Step4: Determine solution type

If $\Delta=0$, the quadratic equation has one real solution.

Answer:

Discriminant: 0
Type of solutions: one real solution