Solving Quadratic Equations in MATLAB & Octave
Solving Quadratic Equations in MATLAB
The solve function can also solve higher order equations. It is often used to solve quadratic equations. The function returns the roots of the equation in an array.
The following example solves the quadratic equation x2 -7x +12 = 0. Create a script file and type the following code −
eq = 'x^2 -7*x + 12 = 0'; s = solve(eq); disp('The first root is: '), disp(s(1)); disp('The second root is: '), disp(s(2));
When you run the file, it displays the following result −
The first root is: 3 The second root is: 4
Solving Quadratic Equations in Octave
The following example solves the quadratic equation x2 -7x +12 = 0 in Octave. Create a script file and type the following code −
s = roots([1, -7, 12]); disp('The first root is: '), disp(s(1)); disp('The second root is: '), disp(s(2));
When you run the file, it displays the following result −
The first root is: 4 The second root is: 3
Solving Higher Order Equations in MATLAB
The solve function can also solve higher order equations. For example, let us solve a cubic equation as (x-3)2(x-7) = 0
solve('(x-3)^2*(x-7)=0')
MATLAB will execute the above statement and return the following result −
ans = 3 3 7
In case of higher order equations, roots are long containing many terms. You can get the numerical value of such roots by converting them to double. The following example solves the fourth order equation x4 − 7x3 + 3x2 − 5x + 9 = 0.
Create a script file and type the following code −
eq = 'x^4 - 7*x^3 + 3*x^2 - 5*x + 9 = 0'; s = solve(eq); disp('The first root is: '), disp(s(1)); disp('The second root is: '), disp(s(2)); disp('The third root is: '), disp(s(3)); disp('The fourth root is: '), disp(s(4)); % converting the roots to double type disp('Numeric value of first root'), disp(double(s(1))); disp('Numeric value of second root'), disp(double(s(2))); disp('Numeric value of third root'), disp(double(s(3))); disp('Numeric value of fourth root'), disp(double(s(4)));
When you run the file, it returns the following result −
The first root is:
6.630396332390718431485053218985
The second root is:
1.0597804633025896291682772499885
The third root is:
- 0.34508839784665403032666523448675 - 1.0778362954630176596831109269793*i
The fourth root is:
- 0.34508839784665403032666523448675 + 1.0778362954630176596831109269793*i
Numeric value of first root
6.6304
Numeric value of second root
1.0598
Numeric value of third root
-0.3451 - 1.0778i
Numeric value of fourth root
-0.3451 + 1.0778i
Please note that the last two roots are complex numbers.
Solving Higher Order Equations in Octave
The following example solves the fourth order equation x4 − 7x3 + 3x2 − 5x + 9 = 0.
Create a script file and type the following code −
v = [1, -7, 3, -5, 9]; s = roots(v); % converting the roots to double type disp('Numeric value of first root'), disp(double(s(1))); disp('Numeric value of second root'), disp(double(s(2))); disp('Numeric value of third root'), disp(double(s(3))); disp('Numeric value of fourth root'), disp(double(s(4)));
When you run the file, it returns the following result −
Numeric value of first root 6.6304 Numeric value of second root -0.34509 + 1.07784i Numeric value of third root -0.34509 - 1.07784i Numeric value of fourth root 1.0598