State the value of the discriminant. Then determine the number of real roots of the equation. n (7n + 8) = - 10

a. - 216, 0 real roots

b. 24, 2 real roots

c. - 226, 2 real roots

d. - 272, 0 real roots

a. - 216, 0 real roots

Step-by-step explanation:

The discriminant of ...

ax² + bx + c = 0

is ...

d = b² - 4ac

When we put your equation into the standard form shown above, we get ...

7n² + 8n + 10 = 0

Then we can identify a=7, b=8, c=10. The discriminant is then ...

d = 8² - 4·7·10 = 64 - 280 = - 216

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The interpretation of the discriminant is ...

<0; no real roots (2 complex one real root (multiplicity 2) > 0; 2 real roots

Your discriminant is - 216, so there are 0 real roots.