Question

find the discriminant.
8t² - 4t + 5 = 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 $at^{2}+bt + c=0$, here $a = 8$, $b=-4$, $c = 5$.

Step2: Calculate the discriminant

The discriminant formula is $\Delta=b^{2}-4ac$. Substitute the values: $\Delta=(-4)^{2}-4\times8\times5$.
$\Delta = 16-160=-144$.

Step3: Determine the type of solutions

If $\Delta>0$, two real solutions; if $\Delta = 0$, one real solution; if $\Delta<0$, two complex (non - real) solutions. Since $\Delta=-144<0$, the equation has two complex (non - real) solutions.

Answer:

Discriminant: $-144$
Type of solutions: two complex (non - real) solutions