Hướng dẫn solve quadratic equation python
Given a quadratic equation the task is solve the equation or find out the roots of the equation. Standard form of quadratic equation is $$ax^2+ bx + c =0$$ where, $a, b$, and $c$ are coefficient and real numbers and also $a \ne 0$ 0. If $a$ is equal to $0$ that equation is not valid quadratic equation. Show See more: Hướng dẫn lập trình Python – Python Guide 1. Python Solve Quadratic Equation Using the Direct FormulaUsing the below quadratic formula we can find the root of the quadratic equation. Let $\Delta =b^2-4ac$, then:
# Python program to find roots of quadratic equation import math # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c # checking condition for dcriminant if d > 0: print("Your equation has real and different roots:") print((-b + math.sqrt(d))/(2 * a)) print((-b - math.sqrt(d))/(2 * a)) elif d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is less than 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", math.sqrt(-d),'i') print(- b / (2 * a), " -", math.sqrt(-d),'i') equationroots() 2. Python Solve Quadratic Equation Using the Complex Math ModuleFirst, we have to calculate the discriminant and then find two solution of quadratic equation using
# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() The standard form of a quadratic equation is: ax2 + bx + c = 0, where a, b and c are real numbers and a ≠ 0 The solutions of this quadratic equation is given by: (-b ± (b ** 2 - 4 * a * c) ** 0.5) / (2 * a) Source Code
Output Enter a: 1 Enter b: 5 Enter c: 6 The solutions are (-3+0j) and (-2+0j) We have imported the You can change the value of a, b and c in the above program and test this program. Given a quadratic equation the task is solve the equation or find out the roots of the equation. Standard form of quadratic equation is – ax2 + bx + c where, a, b, and c are coefficient and real numbers and also a ≠ 0. If a is equal to 0 that equation is not valid quadratic equation. Examples: Input :a = 1, b = 2, c = 1 Output : Roots are real and same -1.0 Input :a = 2, b = 2, c = 1 Output : Roots are complex -0.5 + i 2.0 -0.5 - i 2.0 Input :a = 1, b = 10, c = -24 Output : Roots are real and different 2.0 -12.0 Method 1: Using the direct formula Using the below quadratic formula we can find the root of the quadratic equation. There are following important cases. If b*b < 4*a*c, then roots are complex (not real). For example roots of x2 + x + 1, roots are -0.5 + i1.73205 and -0.5 - i1.73205 If b*b == 4*a*c, then roots are real and both roots are same. For example, roots of x2 - 2x + 1 are 1 and 1 If b*b > 4*a*c, then roots are real and different. For example, roots of x2 - 7x - 12 are 3 and 4
Output: real and different roots 2.0 -12.0 Method 2: Using the complex math module First, we have to calculate the discriminant and then find two solution of quadratic equation using cmath module.
Output: The roots are (-3.414213562373095+0j) (-0.5857864376269049+0j) |