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4 years ago

10

Without using a calculator, determine the number of real zeros of the function

2 answers:

Novay_Z [31]4 years ago

8 0

Answer:

3

Step-by-step explanation:

Papessa [141]4 years ago

7 0

First, we use the rational root theorem to determine any solutions of p(x). <span>= x3 + 4x2 + x − 6</span>

Factoring -6:

1
-1
2
-2
3
-3
6
-6

<span>x = 1 </span>

<span>p(1) = 1^3 + 4 * 1^2 + 1 - 6 = 6 - 6 = 0 </span>
<span>x = 1 is a solution. </span>

(x^3 + 4x^2 + x - 6) / (x - 1) =

x^3 / x = x^2
x^2 * (x - 1) = x^3 - x^2
x^3 + 4x^2 - x^3 + x^2 = 5x^2

5x^2 / x = 5x
5x * (x - 1) = 5x^2 - 5x
5x^2 + x - 5x^2 + 5x = 6x

6x / x = 6
6 * (x - 1) = 6x - 6
6x - 6 - 6x + 6 = 0

<span>(x - 1) * (x^2 + 5x + 6) </span>

x^2 + 5x + 6 factors to (x + 3) * (x + 2)

Factors:

<span>(x - 1) </span>
<span>(x + 2) </span>
<span>(x + 3) </span>

<span>roots: </span>

<span>x = 1 </span>
<span>x = -2 </span>
<span>x = -3</span>

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