In this problem, you will use Bisection method to find a root of a polynomial.

Write a C program to find a root of a cubic polynomial p(x)=a x^3 + b x^2 +c x +d=0 in the interval [-50,50] if it exists. You program will first prompt for and read the coefficients a, b, c, and d of the polynomial.

Step#1: Locate the interval [x0,x1] containing the root as follows:

- fix x0 to -50 . Also initialize x1 to -50

- for each value of x starting from -50 to 50 with increment of 1

• If |p(x)| < epsilon -> display the value of x as the root and stop.
• If p(x)*p(x0)<0 -> assign x to x1 and get outside the loop (using break statement)

Step#2: Finding the root:

• After the loop, if x1 is still 50 -> display No root found inside [-50,50] and terminate
• If not > The root is in the latest interval [x0,x1]. Then apply the following bisection procedure method:
  • Compute xm=(x1+x0)/2 which represents the middle of the interval [x0,x1]
  • While |p(xm)| >= epsilon

• If p(x0)*p(xm) < 0 -> root between x0 and x1, so x1 = xm
• if p(xm)*p(x1) >0 -> root between xm and x1, so x0 = xm
• update xm=(x0+x1)/2

• Display the value of the root found and the number of iterations (repetitions) to obtain the root.

Note: Define epsilon as a constant with a value = 1E-6

Below are 3 sample runs

Enter a,b,c,d of ax^3+bx^2+cx+d=0: 0.5 0.88 -1.2 7.5

The polynominal has root at x=-3.591302

found after 27 iteration

Enter a,b,c,d of ax^3+bx^2+cx+d=0: -2.5 45.2 7.8 55.6

The polynominal has root at x=18.316626

found after35 iteration

Enter a,b,c,d of ax^3+bx^2+cx+d=0: 0.5 87.8 45.2 23.4

No root found in the interval [-50 , 50]

please solve it without function