Download quadratic report

Sample Lab Report:
Define inputs and relationships:
The inputs the user provides will be the coefficients of the quadratic equation
coefa * x 2 + coefb * x + coefc = 0 , coefa, coefb and coefc
There are no constants needed as input to this algorithm.
The value of the root x of the quadratic equation is
− coefB ± coef b 2 − 4 × coefa × coefc
root = x =
2 × coefa
The discriminant of the quadratic equation will be determined to help discriminate between different kinds of
solutions of the quadratic equation. The discriminant is
descri min ant = coef b 2 − 4 × coefa × coefc
Define outputs:
Any one of the following, the output chosen will be determined by the values of the coefficients
1. When the discriminant is < 0, the solutions are imaginary and the following message should be printed to
the output window before the program terminates:
There are no real roots
2. When the discriminant = 0, the solution is a pair of identical roots and the following message should be
printed before the program terminates; Note that the number printed in the message will be the actual
value of the double real root. .
There is one double root, root1 = root2 = 4.00
3. When the discriminant > 0, the solution includes two real roots and the following message should be
printed before the program terminates; Note that the numbers printed in the message will be the actual
values of the two real roots.
There are two real roots, root1 = -1.00 and root2 = 3.00
4. When coefa = 0, the solution is the solution to a linear equation and therefore the solution is a single
root. In the case the following message should be printed. Note that the number in the following
message will be the actual value of the single root
There is one real root, root = 2.00
5. When all coefficients are 0 then any real number can be a root of the quadratic equation. In this case the
following message should be printed.
Every real number is a root
6. When coefa=0, coefb=0, coefc not zero then there is no solution to the quadratic equation. Print the
following message
There are no real roots
State the problem
Assume that the coefficients of a quadratic equation, coefa, coefb and coefc in the equation
coefa * x 2 + coefb * x + coefc = 0 are given, that is they will be supplied by the user of the program. Determine
the real roots of the quadratic equation specified by the given coefficients, or indicate that there are no solutions.
The solution must handle all possible sets of coefficients the user might enter, and must print a message
indicating there are no real roots if all roots of the quadratic equation are complex or if there are no roots of the
quadratic equation. The solution should recognize when there is a repeated root of the quadratic equation, when
there is a single root, and when there are two distinct roots.
Final Detailed Algorithm
Remember the algorithm does not contain language specific information
For your lab report you will submit EITHER a flow chart OR a written list of steps not both. I have
provided a sample of each here in the sample lab report.
Start main
Prompt for confidents using
prompt specified in problem
coefa, coefb, coefc
Print summary of coefficients
using format specified in problem
Calculate discriminant
coefb*coefb - 4*coefa*coefc
coefa = 0
N
discriminant = 0
Y
Y
N
Y
discriminant < 0
N
coefb = 0
Y
root1 =
-coefb /(2*coefa)
N
root1 = (-coefb + discriminant)
/ (2*coefA)
root1 =
-coefC / coefb
There is one real
root which occurs
twice. root1= …..
one real root
root1= …..
coefc = 0
Y
All values of x
are roots
root2 = (-coefb - discriminant)
/ (2*coefa)
The two real roots
are root1=……
and root 2=…..
N
A
There are no real
roots
A
End main
Final Detailed algorithm
1. Prompt for coefa using the prompt
a. “Enter the value of the coefficient of the second order (x
squared) term:”
b. Read the value of coefa
2. Prompt for coefb using the prompt
a. “Enter the value of the coefficient of the first order
term:”
b. Read the value of coefb
3. Prompt for coefa using the prompt
a. “Enter the value of the constant term:”
b. Read the value of coefc
4. Read in coefa, coefb, and coefc, the coefficients of the quadratic equation
5. Print 2 blank lines after your input is complete
6. Print a summary of the input values of the coefficients of the quadratic equation using fixed
point format with three digits after the decimal. The values should be printed within the
following messages (replacing the numbers shown as examples).
The coefficients of the quadratic equation are:
Coefficient of the second order term is 1.323,
Coefficient of the first order term is 3.645,
Coefficient of the constant term is 2.152
7. Print a three blank lines after printing the coefficients
8. Calculate the discriminant: coefb*coefb - 4*coefa*coefc
9. If coefa=0 and coefb=0 and coefc=0 then
a. Print the string “Every real number is a root”
b. Exit the program
10. if coefa = 0 and coefb = 0 and coefc ≠ 0 then
a. Print the string “There are no real roots”
b. Exit the program
11. If coefa= 0 and coefb ≠ 0 then
a. Solve for the single root
-coefc/coefb
b. Print the string “There is one real root, root1 = ”
c. Print the value of the single root
d. Exit the program
12. If the discriminant (b*b=4ac) is zero
a. Calculate the single root -coefb
b. Print the string “There is one double root, root1 = root2 = “
c. Print the value of root1
d. Exit the program
13. If the discriminant (b*b=4ac) is positive
a. Solve the quadratic equation for two identical roots
b. root1 =
− coefb + coef b 2 − 4 × coefa × coefc
2 × coefa
− coefb − coef b 2 − 4 × coefa × coefc
root 2 =
2 × coefa
c. Print the string “There are two real roots, root1 = “
d. Print the value of root 1
e. Print the string “ and root 2 = “
f. Print the value of root2
g. Exit the program
14. If the discriminant (b*b=4ac) is negative
a. The quadratic equation has no real roots.
b. Print the string “There are no real roots”
c. Exit the program
Test plan for quadratic root solver (to be used for grading of your codes)
1.
coefB 2 − 4(coefA)( coefC ) > 0; resulting in two real roots, the common case
Sample test data for this case coefa =5, coefb =9 and coefc =2
Enter the value of the coefficient of the second order (x squared) term:
5.0
Enter the value of the coefficient of the first order term:
9.0
Enter the value of the constant term:
2.0
The coefficients of the quadratic equation are:
Coefficient of the second order term is 5.000
Coefficient of the first order term is 9.000,
Coefficient of the constant term is 2.000
There are two real roots, root1 = -0.26 and root2 = -1.54.
2. coefB 2 − 4(coefA)( coefC ) < 0; resulting in imaginary roots (no real roots)
Sample test data for this case coefa =3, coefb =4 and coefc =5
Enter the value of the coefficient of the second order (x squared) term:
3.0
Enter the value of the coefficient of the first order term:
4.0
Enter the value of the constant term:
5.0
The coefficients of the quadratic equation are:
Coefficient of the second order term is 3.000
Coefficient of the first order term is 4.000,
Coefficient of the constant term is 5.000
There are no real roots.
3. coefB 2 − 4(coefA)( coefC ) = 0; resulting in two identical real roots
Equation for the solution for the root is x = - coeffB / ( 2 * coeffA )
Sample test data for this case coefa =4, coefb =8 and coefc =4
Enter the value of the coefficient of the second order (x squared) term:
4.0
Enter the value of the coefficient of the first order term:
8.0
Enter the value of the constant term:
4.0
The coefficients of the quadratic equation are:
Coefficient of the second order term is 4.000
Coefficient of the first order term is 8.000,
Coefficient of the constant term is 4.000
There is one double root, root1 = root2 = -1.00.
4. coefa =0 coefb ≠0
Equation for the solution for the root is x = - coefc / coefb
Prints: one real root, root1= and the value of the root
Sample test data for this case coefa = 0.0, coefb = 5.0, coefc = 25.0
Enter the value of the coefficient of the second order (x squared) term:
0.0
Enter the value of the coefficient of the first order term:
5.0
Enter the value of the constant term:
25.0
The coefficients of the quadratic equation are:
Coefficient of the second order term is 0.000
Coefficient of the first order term is 5.000,
Coefficient of the constant term is 25.000
There is one real root, root1 = -5.00.
5. coefa =0 coefb = 0 coefc =0
The quadratic equation reduces to 0.0 = 0.0; all values of x are roots
Prints all values of x are roots of the equation
Sample test data for this case coefa = 0.0, coefb = 0.0, coefc =0.0
Enter the value of the coefficient of the second order (x squared) term:
0.0
Enter the value of the coefficient of the first order term:
0.0
Enter the value of the constant term:
0.0
The coefficients of the quadratic equation are:
Coefficient of the second order term is 0.000
Coefficient of the first order term is 0.000,
Coefficient of the constant term is 0.000
All values of x are roots
6. coefa =0 coefb = 0 coefc ≠0
The quadratic equation reduces to coefc = 0.0. If coefc is not zero the equation has no solutions.
Prints “There are no real roots”
Sample test data for this case coefa = 0.0, coefb = 0.0, coefc = 25.0
Enter the value of the coefficient of the second order (x squared) term:
0.0
Enter the value of the coefficient of the first order term:
0.0
Enter the value of the constant term:
25.0
The coefficients of the quadratic equation are:
Coefficient of the second order term is 0.000
Coefficient of the first order term is 0.000,
Coefficient of the constant term is 25.000
There are no real roots