# Program for Polynomial Solution without Formula, Numerical Analysis

## Given a polynomial equation, write a program to check whether one of its roots lies within a given range. No formula, such as the quadratic formula for binomials is to be used.

Last Reviewed and Updated on February 7, 2020

## C/C++ Program for Polynomial Solution without Formula, Numerical Analysis

Determine whether the following quadratic equation has a root between -1.0 and +1.0. If it exists, print that root to an accuracy of two decimal places. Do not use the quadratic formula. The equation is: 4x2 + 10x - 9 = 0

```#include <iostream>

using namespace std;

int main()
{
int counter = 0;

// start from x = -1.0f
float x = -1.0f;

while(true)
{
// increment by 0.001
// small steps -1.0, -.999, -.998, and so on
x += 0.001f;

// check after 100 increments
if(counter++ == 100)
{
// if x has become larger than
// 1 quit
if(x > 1.0f)
{
cout << "No solution in -1 and +1";

return 0;
}

// set increment counter to zero
counter = 0;

}

cout << "x = " << x << endl;

// caculate the equation expression
float equation = (4 * x * x) + (10 * x) - 9;

// make absolute, positive
if(equation < 0)
{
equation *= -1;
}

// if it is almost zero
// we have the solution
if(equation < 0.01)
{
cout << "root = " << x << endl;

break;
}

}

return 0;
}```

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