7. [lWrite a program to estimate the real roots of a cubic polynomial function u

Question

7. [lWrite a program to estimate the real roots of a cubic polynomial function using incremetal search. f(a) Subinterval f(b) -Original interval A cubic polynomial has the fomm y f(-r ar.a, The following are the refinements of the program in pseudo code. main: read coefficients, interval endpoints a and b, and stop aize compute the number of subintervals, n set k to while kn-1 compute left subinterval endpoint compute right subinterval endpoint check_roota(lert,right, coetricianta) increment k by 1 check xoots(b,,coeffieients) check_roots (left,right, coefficients): set f-left poly(left, coefficients} se _right to poly (right, coetticianta) 1f f 1eft is near zero print root at left endpoint else i iattright print roor at midpoint of subimerval poly(x,0,1,2.a3): return aox3 + a1x2 a a3

Explanation / Answer

#include <stdio.h>

#include <math.h>

int main()

{

    double a, b, c, determinant, root1,root2, realPart, imaginaryPart;

    printf("Enter coefficients a, b and c: ");

    scanf("%lf %lf %lf",&a, &b, &c);

    determinant = b*b-4*a*c;

    // condition for real and different roots

    if (determinant > 0)

    {

    // sqrt() function returns square root

        root1 = (-b+sqrt(determinant))/(2*a);

        root2 = (-b-sqrt(determinant))/(2*a);

        printf("root1 = %.2lf and root2 = %.2lf",root1 , root2);

    }

    //condition for real and equal roots

    else if (determinant == 0)

    {

        root1 = root2 = -b/(2*a);

        printf("root1 = root2 = %.2lf;", root1);

    }

    // if roots are not real

    else

    {

        realPart = -b/(2*a);

        imaginaryPart = sqrt(-determinant)/(2*a);

        printf("root1 = %.2lf+%.2lfi and root2 = %.2f-%.2fi", realPart, imaginaryPart, realPart, imaginaryPart);

    }

    return 0;

}

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