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?

4 次查看（过去 30 天）
Shashank Shekhar
Shashank Shekhar 2021-10-1
评论： Shashank Shekhar 2021-10-2
% 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;
  1 个评论
Mathieu NOE
Mathieu NOE 2021-10-1
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.

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

Chunyu Xiao
Chunyu Xiao 2021-10-1
Ran in:
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

类别

在 Help Center 和 File Exchange 中查找有关 Polynomials 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by