A quadratic equation is a polynomial equation of degree 2, commonly written in the form p(x)...

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A quadratic equation is a polynomial equation of degree 2, commonly written in the form p(x) = ax2 + bx + c, where x is a variable and a, b, c are called the coefficients of the equation. A homogeneous quadratic equation is one that is set equal to 0, e.g., p(x) =3.1x2 + 2x ? 5 = 0. Note that the coefficients in this problem are positive or negative real numbers (they could be complex numbers, but we will assume they are real numbers). If x is a real number and p(x) is 0 then x is called a root of the equation. In general, a polynomial of degree n (the degree of a polynomial equation is the value of the largest exponent) will have n roots, so a quadratic equation will have two roots. However, depending on the values of the coefficients, some or all of these roots may be complex (i.e.,not real numbers). The well-known quadratic formula can be used to determine the two real roots of a quadratic equation-if they exist,The b2? 4ac term under the radical is called the discriminant, and if the discriminant is greater than or equal to zero, then both roots are real. A sample run is shown below. Your program should be similar (user input is shown in bold). Enter coefficient a: 2.5 Enter coefficient b: 6.7 Enter coefficient c: -3 2.5x^2 + 6.7x + -3 = 0 Root1 = 0.39078 Root2 = -3.07078 Implement the following pseudocode. Include necessary header files Function discriminant (Input: a is Double, b is Double, c is Double) Returns Double Return b2 - 4ac End Function discriminant Function root1 (Input: a is Double, b is Double, c is Double) Returns Double disc ? discriminant (a, b, c) Return [ -b+sqrt (disc)]/(2a) End Function root1 Function root2 (Input: a is Double, b is Double, c is Double) Returns Double disc ? discriminant (a, b, c) Return [ -b - sqrt (disc)]/(2a) End Function root2 Function display_eqn (Input: a is Double, b is Double, c is Double) Returns Nothing Display a "x^2 + "b"x + "c" =0" End Function display_eqn Function main (Input: Nothing) Define necessary variables Display prompt "Enter coefficient for a: " a ? Read real number Display prompt "Enter coefficient for b: " b? Read real number Display prompt "Enter coefficient for c: " c? Read real number r1 ? root1 (a, b, c) r2? root2 (a, b, c) Call display_eqn (a, b, c) Display "Root1 = " r1 Display "Root2 = "r2 End Function main A quadratic equation is a polynomial equation of degree 2, commonly written in the form p(x) = ax2 + bx + c, where x is a variable and a, b, c are called the coefficients of the equation. A homogeneous quadratic equation is one that is set equal to 0, e.g., p(x) =3.1x2 + 2x ? 5 = 0. Note that the coefficients in this problem are positive or negative real numbers (they could be complex numbers, but we will assume they are real numbers). If x is a real number and p(x) is 0 then x is called a root of the equation. In general, a polynomial of degree n (the degree of a polynomial equation is the value of the largest exponent) will have n roots, so a quadratic equation will have two roots. However, depending on the values of the coefficients, some or all of these roots may be complex (i.e.,not real numbers). The well-known quadratic formula can be used to determine the two real roots of a quadratic equation-if they exist,The b2? 4ac term under the radical is called the discriminant, and if the discriminant is greater than or equal to zero, then both roots are real. A sample run is shown below. Your program should be similar (user input is shown in bold). Enter coefficient a: 2.5 Enter coefficient b: 6.7 Enter coefficient c: -3 2.5x^2 + 6.7x + -3 = 0 Root1 = 0.39078 Root2 = -3.07078 Implement the following pseudocode. Include necessary header files Function discriminant (Input: a is Double, b is Double, c is Double) Returns Double Return b2 - 4ac End Function discriminant Function root1 (Input: a is Double, b is Double, c is Double) Returns Double disc ? discriminant (a, b, c) Return [ -b+sqrt (disc)]/(2a) End Function root1 Function root2 (Input: a is Double, b is Double, c is Double) Returns Double disc ? discriminant (a, b, c) Return [ -b - sqrt (disc)]/(2a) End Function root2 Function display_eqn (Input: a is Double, b is Double, c is Double) Returns Nothing Display a "x^2 + "b"x + "c" =0" End Function display_eqn Function main (Input: Nothing) Define necessary variables Display prompt "Enter coefficient for a: " a ? Read real number Display prompt "Enter coefficient for b: " b? Read real number Display prompt "Enter coefficient for c: " c? Read real number r1 ? root1 (a, b, c) r2? root2 (a, b, c) Call display_eqn (a, b, c) Display "Root1 = " r1 Display "Root2 = "r2 End Function main

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