Question

find the discriminant.
w² + 4w + 4 = 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 $aw^{2}+bw + c = 0$, the discriminant $\Delta=b^{2}-4ac$. In the equation $w^{2}+4w + 4 = 0$, $a = 1$, $b = 4$, and $c = 4$.

Step2: Calculate the discriminant

Substitute $a = 1$, $b = 4$, $c = 4$ into the formula: $\Delta=(4)^{2}-4\times1\times4$.
$\Delta = 16 - 16=0$.

Step3: Determine the type of solutions

If $\Delta>0$, the equation has two real - solutions. If $\Delta = 0$, the equation has one real solution. If $\Delta<0$, the equation has two complex (non - real) solutions. Since $\Delta = 0$, the equation has one real solution.

Answer:

Discriminant: 0
Type of solutions: one real solution