C Program for Quadratic Equation Roots

2024-05-22 23:28| 来源: 网络整理| 查看: 265

In this article, we will learn to write a C program to find the roots of the quadratic equation.

Quadratic Equation is polynomial equations that have a degree of two, which implies that the highest power of the function is two. The quadratic equation is represented by ax2 + bx + c where a, b, and c are real numbers and constants, and a ≠ 0. The root of the quadratic equations is a value of x that satisfies the equation.

How to Find Quadratic Equation Roots?

The Discriminant is the quantity that is used to determine the nature of roots:

Discriminant(D) = b2 - 4ac;

Based on the nature of the roots, we can use the given formula to find the roots of the quadratic equation.

1. If D > 0, Roots are real and different $root1 = \dfrac{-b +\sqrt{(b^2 - 4ac)}}{2a}$ $root2 = \dfrac{-b -\sqrt{(b^2 - 4ac)}}{2a}$ 2. If D = 0, Roots are real and the same $root1 = root2 = \dfrac{-b}{2a}$ 3.If D < 0, Roots are complex $root1 = \dfrac{-b}{2a} + \dfrac{i\sqrt{-(b^2 -4ac)}}{2a}$ $root2 = \dfrac{-b}{2a} - \dfrac{i\sqrt{-(b^2 -4ac)}}{2a}$ Program to Find Roots of a Quadratic Equation C // C program to find roots of // a quadratic equation #include #include #include // Prints roots of quadratic // equation ax*2 + bx + x void findRoots(int a, int b, int c) { // If a is 0, then equation is // not quadratic, but linear if (a == 0) { printf("Invalid"); return; } int d = b * b - 4 * a * c; double sqrt_val = sqrt(abs(d)); if (d > 0) { printf("Roots are real and different\n"); printf("%f\n%f", (double)(-b + sqrt_val) / (2 * a), (double)(-b - sqrt_val) / (2 * a)); } else if (d == 0) { printf("Roots are real and same\n"); printf("%f", -(double)b / (2 * a)); } else // d < 0 { printf("Roots are complex\n"); printf("%f + i%f\n%f - i%f", -(double)b / (2 * a), sqrt_val / (2 * a), -(double)b / (2 * a), sqrt_val / (2 * a)); } } // Driver code int main() { int a = 1, b = -7, c = 12; // Function call findRoots(a, b, c); return 0; }

Output

Roots are real and different 4.000000 3.000000Complexity Analysis

Time Complexity: O(log(D)), where D is the discriminant of the given quadratic equation.

Auxiliary Space: O(1)

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