for eqn y=x^2 +bx +c, I have a known variable matrix for y. How can I find the value of x for corresponding different value of y in matrix?

% we know how to find the value of x by varying x using linspace and calculating corresponding value of y.

% But the problem is that i know the 50 different value of y and i have to find corresponding value of x. How can i do that?

load value_y

y=x.^2+b*x+c;

[Mathieu NOE]

hello

this is not a matlab question

this is solving a second order polynomial equation - put the resolution method in a unction and apply it to your y data (array)

A second degree polynomial, also referred as a quadratic equation can be expressed as below:

ax² + bx + c = 0

to solve the equation we can use the quadratic formulas as shown below:

x1 = (-b + sqrt(b²-4ac))(2a)

x2 = (-b - sqrt(b²-4ac))/(2a)

a quadratic equation has two solutions when b²-4ac > 0

a quadratic equation has only one solution when b²-4ac = 0

a quadratic equation has no solution when b²-4ac < 0

Example (2 solutions)

2x²+ 6x + 1 = 0

b²-4ac = 62-4 x 2 x 1 = 28, since 28 > 0, we can conclude that there exists two solutions

x1 = (-b + (b²-4ac)1/2)/2a = -0.177

x2 = (-b - (b²-4ac)1/2)/2a = -2.822

Example (1 solutions)

3x² + 6x + 3 = 0

b²-4ac = 62-4 x 3 x 3 = 0, thus we can conclude that there only exists one solution

x = -b/2a = -1

How to construct a quadratic equation when its solutions are given

if x1 = 3 and x2 = 2, then we can construct the equation as shown below:

p(x) = (x - x1)(x - x2) = (x - 3)(x - 2) = x² - 5x + 6 = 0.

Answer 1

[Chunyu Xiao]

You can use roots to solve the problem:

% example
b = 2;
c = -3;

N = 50;
y = (1:N)';
x = zeros(N,2);
for k = 1:N
    x(k,:) = roots([1,b,c-y(k)]);
end
table(y,x)

ans = 50×2 table
    y             x         
    __    __________________

     1    -3.2361     1.2361
     2    -3.4495     1.4495
     3    -3.6458     1.6458
     4    -3.8284     1.8284
     5         -4          2
     6    -4.1623     2.1623
     7    -4.3166     2.3166
     8    -4.4641     2.4641
     9    -4.6056     2.6056
    10    -4.7417     2.7417
    11     -4.873      2.873
    12         -5          3
    13    -5.1231     3.1231
    14    -5.2426     3.2426
    15    -5.3589     3.3589
    16    -5.4721     3.4721

[Shashank Shekhar]

thanks