quadratic operator +( const quadratic& q1, const quadratic& q2 ); // Postcondition: The return value is the // quadratic expression obtained by adding // q1 and q2. For example, the c coefficient // of the return value is the sum of ql's c // coefficient and q2's c coefficient. quadratic operator *( double r, const quadratic& q ); // Postcondition: The return value is the // quadratic expression obtained by // multiplying each of q's // coefficients by the number r. Notice that the left argument of the overloaded operator* is a double number (rather than a qua- dratic expression). This allows expressions such as 3.14 * q, where q is a quadratic expression. This project is a continuation of the previous 9 project. For a quadratic expression such as ax² + bx+c, a real root is any double number .x such that ax²+bx+c = 0. For example, the quadratic expression 2x² + 8x +6 has one of its real roots at x = -3, because substituting x = -3 in the formula 2x² + 8x+6 yields the value: 2× (-3²) +8 × (-3) +6 = 0 There are six rules for finding the real roots of a qua- dratic expression: (1) If a, b, and c are all zero, then every value of x is a real root. (2) If a and bare zero, but c is nonzero, then there are no real roots. (3) If a is zero, and bis nonzero, then the only real root is x = -c/b. (4) If a is nonzero and b² <4ac, then there are no real roots. (5) If a is nonzero and b² = 4ac, then there is one real root x = -b/2a. (6) If a is nonzero, and b²2>4ac, then there are two real roots: x = -b-√√b². 2a - 4ac _b+√√b²-4ac 2a Write a new member function that returns the num- ber of real roots of a quadratic expression. This an- swer could be 0, or 1, or 2, or infinity. In the case of an infinite number of real roots, have the member function return 3. (Yes, we know that 3 is not infin- ity, but for this purpose it is close enough!) Write two other member functions that calculate and re- turn the real roots of a quadratic expression. The pre- condition for both functions is that the expression has at least one real root. If there are two real roots, then one of the functions returns the smaller of the two roots, and the other function returns the larger of the two roots. If every value of x is a real root, then both functions should return zero. 10 Specify, design, and implement a class that can be used to simulate a lunar lander, which is a small spaceship that transports astro- nauts from lunar orbit to the surface of the moon. When a lunar lander is constructed, the following items should be specified, with default values as in- dicated: (1) Current fuel flow rate as a fraction of the maximum fuel flow (default zero) (2) Vertical speed of the lander (default zero meters/sec) (3) Altitude of the lander (default 1000 meters) (4) Amount of fuel (default 1700 kg) (5) Mass of the lander when it has no fuel (de- fault 900 kg) (6) Maximum fuel consumption rate (default 10 kg/sec) (7) Maximum thrust of the lander's engine (de- fault 5000 newtons) Don't worry about other properties (such as horizon- tal speed). The lander has constant member functions that allow a program to retrieve the current values of any of these seven items. There are only two modifica- tion member functions, described next. The first modification function changes the current fuel flow rate to a new value ranging from 0.0 to 1.0. This value is expressed as a fraction of the maximum fual flom