Question

Use the intermediate value theorem to choose an interval over which the function, f(x)=2x^3 - 3x +5 is guaranteed to have a zero.

Answer 1

Answer:

The answer is c. {0,2).

Step-by-step explanation:

Answer 2

An interval over which the function, f(x) = -2x³ - 3x +5 is guaranteed to have a zero is [0,2]

Further explanation

If equation ax³ + bx² + cx + d = 0 has roots x₁ , x₂ , and x₃ then

$x_1 + x_2 + x_3 = - \frac{b}{a}$

$x_1 x_2 + x_1 x_3 + x_2 x_3 = \frac{c}{a}$

$x_1 x_2 x_3 = - \frac{d}{a}$

Let us now tackle the problem!

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Given:

$f(x) = -2x^3 - 3x + 5$

Option A:

$f(x) = -2x^3 - 3x + 5$

$f(-3) = -2(-3)^3 - 3(-3) + 5 = 68$

$f(-2) = -2(-2)^3 - 3(-2) + 5 = 27$

Because both of the value of f(-3) and f(-2) are positive , we cannot guarateed the value of the function will be zero at interval [-3,-2]

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Option B:

$f(x) = -2x^3 - 3x + 5$

$f(0) = -2(0)^3 - 3(0) + 5 = 5$

$f(-2) = -2(-2)^3 - 3(-2) + 5 = 27$

Because both of the value of f(0) and f(-2) are positive , we cannot guarateed the value of the function is zero at interval [-3,-2]

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Option C:

$f(x) = -2x^3 - 3x + 5$

$f(0) = -2(0)^3 - 3(0) + 5 = 5$

$f(2) = -2(2)^3 - 3(2) + 5 = -17$

Because the value of f(0) and f(2) have different sign , we can guarateed the value of the function will be zero at interval [0,2] , i.e. there is zero between 5 and -17 → -17 < 0 < 5

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Option D:

$f(x) = -2x^3 - 3x + 5$

$f(4) = -2(4)^3 - 3(4) + 5 = -135$

$f(2) = -2(2)^3 - 3(2) + 5 = -17$

Because both of the value of f(4) and f(2) are negatve , we cannot guarateed the value of the function is zero at interval [2,4]

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Learn more

• Solving Quadratic Equations by Factoring : brainly.com/question/12182022
• Determine the Discriminant : brainly.com/question/4600943
• Formula of Quadratic Equations : brainly.com/question/3776858

Answer details

Grade: High School

Subject: Mathematics

Chapter: Polynomial

Keywords: Quadratic , Equation , Discriminant , Real , Number