An interval over which the function, f(x) = -2x³ - 3x +5 is guaranteed to have a zero is [0,2]
<h3>Further explanation</h3>
<em>If equation ax³ + bx² + cx + d = 0 has roots x₁ , x₂ , and x₃ then</em>



Let us now tackle the problem!

Given:

<h2>Option A:</h2>



<em>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]</em>

<h2>Option B:</h2>



<em>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]</em>

<h2>Option C:</h2>



<em>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</em>

<h2>Option D:</h2>



<em>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]</em>

<h3>Learn more</h3>
<h3>Answer details</h3>
Grade: High School
Subject: Mathematics
Chapter: Polynomial
Keywords: Quadratic , Equation , Discriminant , Real , Number