Question

4 find the discriminant of each quadratic equation then state the number and type of solutions. \\(-9n^2 + n - 10 = 0\\) the discriminant is \\(\boxed{}\\), and there is/are \\(\boxed{}\\) \\(\boxed{}\\) solution(s).

Explanation:

Step1: Identify a, b, c values

For $-9n^2 + n - 10 = 0$, $a=-9$, $b=1$, $c=-10$

Step2: Apply discriminant formula

Discriminant: $\Delta = b^2 - 4ac$
$\Delta = 1^2 - 4(-9)(-10)$

Step3: Calculate the discriminant

$\Delta = 1 - 360 = -359$

Step4: Analyze discriminant sign

Negative discriminant means 2 non-real (complex) solutions.

Answer:

The discriminant is $\boldsymbol{-359}$, and there is/are $\boldsymbol{2}$ $\boldsymbol{complex\ (non-real)}$ solution(s).