Question

find the discriminant.
4r² - 4 = 0
what type of solutions does the equation have?
one real solution
two real solutions
two complex (non - real) solutions

Explanation:

Step1: Identify coefficients

For the quadratic equation $ax^{2}+bx + c = 0$, rewrite $4r^{2}-4 = 0$ as $4r^{2}+0r - 4=0$, so $a = 4$, $b = 0$, $c=-4$.

Step2: Calculate discriminant

The discriminant formula is $\Delta=b^{2}-4ac$. Substitute $a = 4$, $b = 0$, $c=-4$ into it: $\Delta=(0)^{2}-4\times4\times(-4)=0 + 64=64$.

Step3: Determine solution type

Since $\Delta>0$, the quadratic - equation has two real solutions.

Answer:

Discriminant: 64
Type of solutions: two real solutions