Question

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

Answer 1

a. -216, 0 real roots

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 roots)
• = 0; one real root (multiplicity 2)
• > 0; 2 real roots

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