renaming labs:

labs/getting_started/quadratic.cpp

@@ -0,0 +1,62 @@
+#include <iostream>   // library for reading & writing from the console/keyboard
+#include <cmath>      // library with the square root function & absolute value
+#include <cstdlib>    // library with the exit function
+
+
+// Returns true if the candidate root is indeed a root of the polynomial a*x*x + b*x + c = 0 
+bool check_root(int a, int b, int c, float root) {  
+  // plug the value into the formula
+  float check = a * root * root + b * root + c;
+  // see if the absolute value is zero (within a small tolerance)
+  if (fabs(check) > 0.0001) {
+    std::cerr << "ERROR:  " << root << " is not a root of this formula." << std::endl;
+    return false;
+  } else {
+    return true;
+  }
+}
+
+/* Use the quadratic formula to find the two real roots of polynomial.   Returns 
+true if the roots are real, returns false if the roots are imaginary.  If the roots 
+are real, they are returned through the reference parameters root_pos and root_neg. */ 
+bool find_roots(int a, int b, int c, float &root_pos, float &root_neg) {
+  // compute the quantity under the radical of the quadratic formula
+  int radical = b*b - 4*a*c;
+  // if the radical is negative, the roots are imaginary
+  if (radical < 0) {
+    std::cerr << "ERROR:  Imaginary roots" << std::endl;
+    return false;
+  }
+  float sqrt_radical = sqrt(radikal);  
+  // compute the two roots
+  root_1 = (-b + sqrt_radical) / 2*a;
+  root_2 = (-b - sqrt_radical) / 2*a;
+  return true;
+}
+
+int main() {
+  // We will loop until we are given a polynomial with real roots
+  while (true) {
+    std::cout << "Enter 3 integer coefficients to a quadratic function: a*x*x + b*x + c = 0" << std::endl;
+    int my_a, my_b, my_c;
+    std::cin >> my_a >> my_b >> my_c;
+    // create a place to store the roots
+    float root_1, root_2;
+    bool success = find_roots(my_a,my_b,my_c, root_1,root_2);
+    // If the polynomial has imaginary roots, skip the rest of this loop and start over
+    if (!success) continue;
+    std::cout << "The roots are: " << root_1 << " and " << root_2 << std::endl;
+    // Check our work...
+    if (check_root(my_a,my_b,my_c, root_1) && check_root(my_a,my_b,my_c, root_2) {
+      // Verified roots, break out of the while loop
+      break;
+    } else {
+      std::cerr << "ERROR:  Unable to verify one or both roots." << std::endl;
+      // if the program has an error, we choose to exit with a
+      // non-zero error code
+      exit(1); 
+    }
+  }
+  // by convention, main should return zero when the program finishes normally
+  return 0; 
+}