Question

Find a real root of the equation x3 + x2 - 100 = 0

Answer 1

Step-by-step explanation:

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Answer 2

-1/3 is a real root of the equation $x^{3} + x^{2} - 100 = 0$

Given:

$x^{3} + x^{2} - 100 = 0$

To find:

A real root of the equation

Solution:

The cubic formula states that for a cubic polynomial $ax^{3} + bx^{2} +cx + d = 0$ where a, b, c and d are constants, the root can be found as follows:

$x = \frac{(-b + \sqrt[2]{(b^{2} - 3ac)} )}{3a}$

In the given equation $x^{3} + x^{2} - 100 = 0$,

a = 1

b = 1

c = 0

d = -1000

Substituting these values in the cubic formula, we get

$x = \frac{(-1 + \sqrt[2]{((-1)^{2} - 3*1*0)} )}{3*1}$

=> $x = \frac{(-1 + \sqrt[2]{1} )}{3}$

=> x = -1/3

Note that this root is not necessarily the only real root of the equation - there may be additional real roots, or there may be no additional real roots. To determine the complete set of real roots, a more sophisticated mathematical tool, such as a root-finding algorithm can be used.

Hence, -1/3 is a real root of the equation $x^{3} + x^{2} - 100 = 0$

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