(C syntax) real number root of a quadratic equation, real number of a quadratic equation

(C syntax) real number root of a quadratic equation, real number of a quadratic equation

Knowledge point:

Mathematical function header file # include <math. h>

Square functions, sqrt ()

Note the difference between equal sign = and value =

 

Content: returns the real number root of an unary quadratic equation (the quadratic system is not 0) ax2 + bx + c = 0 (a =0 ).

Input description:

Three coefficients in one row (separated by spaces)

Output description:

 

First output (-B + sqrt ()/2/a root, one row per row, if it is equal to the real root, output one (both retain two decimal places)

. If there is No real root output, No answer!

 

Input example:

1 1 2

Output example:

No answer!

 

 1 #include <stdio.h> 2 #include <math.h> 3 int main() 4 { 5  float a,b,c,d,x1,x2; 6  scanf("%f %f %f",&a,&b,&c); 7  d=b*b-4*a*c; 8  if (d>=0) 9  {10   x1=(-b+sqrt(d))/(2*a);11   x2=(-b-sqrt(d))/(2*a);12   if(x1==x2)13   {14    printf("%.2f\n",x1);15   }16   else17   {18    printf("%.2f\n%.2f\n",x1,x2);19   }20  }21  else 22  {23   printf("No answer!\n");24  }25  return 0;26 }

 

If there are two equal real numbers for the quadratic equation a (1 + x ^ 2) + 2bx = c (^ 2) of x, judge the shape of a triangle with the edge length a, B, and c

Simplification, (a + c) x ^ 2 + 2bx + a-c = 0
△= 0, (2b) ^ 2-4 (a + c) (a-c) = 0. a ^ 2 = B ^ 2 + c ^ 2
Right Triangle.

A mathematical problem proves that a B c is the three sides of △abc, and a quadratic equation (a-c) x square-2 (a-B) x + a + c-2b = 0 has two real numbers

[The question should be "there are two equal real numbers "]

(A-c) x ^ 2-2 (a-B) x + a + c-2b = 0 has two [equal] real number roots
Discriminant [-2 (a-B)] ^ 2-4 * (a-c) * (a + c-2b) = 0
(A-B) ^ 2-(a-c) * (a + c-2b) = 0
B ^ 2-2bc + c ^ 2 = 0
(B-c) ^ 2 = 0
B = c, isosceles triangle