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Oduvanchick [21]
4 years ago
8

How many real roots does

2+7x+14=0" alt="x^4-x^3-9x^2+7x+14=0" align="absmiddle" class="latex-formula"> have?
A) 1
B) 2
C) 3
D) 4
Mathematics
1 answer:
Leto [7]4 years ago
7 0

Answer: D) 4

<u>Step-by-step explanation:</u>

x⁴ - x³ - 9x² + 7x + 14 = 0

possible rational roots are: ±{1, 2, 7, 14}

Try x = -1

-1  |   1   -1   -9   7   14

   <u>|   ↓  -1     2   7   -14</u>

       1   -2    -7   14   0 ← remainder is 0 so x = -1 is a root

Let's try x = 2 with the factored polynomial

2  |  1   -2   -7   14

   <u>|  ↓    2   0   -14 </u>

       1    0   -7    0  ← remainder is 0 so x = 2 is a root

Factored polynomial x² - 7 can be factored to:

(x - √7) (x + √7)

⇒ x = √7   and x = -√7

The roots are x = {-1, 2, √7, -√7) which are all real numbers.

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3 years ago
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