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.

The answer is c. {0,2).

Step-by-step explanation:

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

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

Let us now tackle the problem!

Given:

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]

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]

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

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]

Grade: High School

Subject: Mathematics

Chapter: Polynomial

Keywords: Quadratic , Equation , Discriminant , Real , Number