Write down the algorithm for the following questions.a) to calculate the root of a quadratic equation.b) to read the roll no, name and marks of three subjects and calculate the total,percentage and division.c) to check whether a triangle can be formed with the given values for the angles.d) to compute the sum of the first “N” natural numbers.e) to display the multiplication table for a given integer.f) to calculate the factorial of a given number.g) to check whether a given number is an Armstrong number or not.h) to determine whether a given number is prime or not.

a) Algorithm to calculate the root of a quadratic equation:

1. Start
2. Declare variables a, b, c, D, x1, x2, realPart, imaginaryPart.
3. Read the values of a, b, c.
4. Calculate the discriminant D = b^2 - 4ac.
5. If D >= 0, calculate x1 = (-b + sqrt(D)) / (2a) and x2 = (-b - sqrt(D)) / (2a).
6. If D < 0, calculate realPart = -b / (2a) and imaginaryPart = sqrt(-D) / (2a).
7. Display the roots.
8. End

b) Algorithm to read the roll no, name and marks of three subjects and calculate the total, percentage and division:

1. Start
2. Declare variables roll_no, name, marks1, marks2, marks3, total, percentage.
3. Read the values of roll_no, name, marks1, marks2, marks3.
4. Calculate total = marks1 + marks2 + marks3.
5. Calculate percentage = (total / 300) * 100.
6. If percentage >= 60, division = 'First'.
7. Else if percentage >= 50, division = 'Second'.
8. Else if percentage >= 40, division = 'Third'.
9. Else division = 'Fail'.
10. Display roll_no, name, total, percentage, division.
11. End

c) Algorithm to check whether a triangle can be formed with the given values for the angles:

1. Start
2. Declare variables angle1, angle2, angle3.
3. Read the values of angle1, angle2, angle3.
4. If angle1 + angle2 + angle3 == 180, display 'Triangle is possible'.
5. Else display 'Triangle is not possible'.
6. End

d) Algorithm to compute the sum of the first “N” natural numbers:

1. Start
2. Declare variables N, sum.
3. Read the value of N.
4. Calculate sum = N * (N + 1) / 2.
5. Display sum.
6. End

e) Algorithm to display the multiplication table for a given integer:

1. Start
2. Declare variables N, i.
3. Read the value of N.
4. For i = 1 to 10, display N * i.
5. End

f) Algorithm to calculate the factorial of a given number:

1. Start
2. Declare variables N, factorial.
3. Read the value of N.
4. Set factorial = 1.
5. For i = 1 to N, calculate factorial = factorial * i.
6. Display factorial.
7. End

g) Algorithm to check whether a given number is an Armstrong number or not:

1. Start
2. Declare variables N, temp, remainder, result.
3. Read the value of N.
4. Set temp = N and result = 0.
5. While temp != 0, calculate remainder = temp % 10, result = result + remainder^3, temp = temp / 10.
6. If result == N, display 'Armstrong number'.
7. Else display 'Not an Armstrong number'.
8. End

h) Algorithm to determine whether a given number is prime or not:

1. Start
2. Declare variables N, i, flag.
3. Read the value of N.
4. Set flag = 0.
5. For i = 2 to sqrt(N), if N % i == 0, set flag = 1 and break.
6. If flag == 0, display 'Prime number'.
7. Else display 'Not a prime number'.
8. End

a) Algorithm to calculate the root of a quadratic equation:

1. Start
2. Declare variables a, b, c, D, x1, x2, realPart, imaginaryPart.
3. Read the values of a, b, c.
4. Calculate the discriminant D = b^2 - 4ac.
5. If D >= 0, calculate x1 = (-b + sqrt(D)) / (2a) and x2 = (-b - sqrt(D)) / (2a).
6. If D < 0, calculate realPart = -b / (2a) and imaginaryPart = sqrt(-D) / (2a).
7. Display the roots.
8. End

b) Algorithm to read the roll no, name and marks of three subjects and calculate the total, percentage and division:

1. Start
2. Declare variables roll_no, name, marks1, marks2, marks3, total, percentage.
3. Read the values of roll_no, name, marks1, marks2, marks3.
4. Calculate total = marks1 + marks2 + marks3.
5. Calculate percentage = (total / 300) * 100.
6. If percentage >= 60, division = 'First'.
7. Else if percentage >= 50, division = 'Second'.
8. Else if percentage >= 40, division = 'Third'.
9. Else division = 'Fail'.
10. Display roll_no, name, total, percentage, division.
11. End

c) Algorithm to check whether a triangle can be formed with the given values for the angles:

1. Start
2. Declare variables angle1, angle2, angle3.
3. Read the values of angle1, angle2, angle3.
4. If angle1 + angle2 + angle3 == 180, display 'Triangle can be formed'.
5. Else display 'Triangle cannot be formed'.
6. End

d) Algorithm to compute the sum of the first “N” natural numbers:

1. Start
2. Declare variables N, sum.
3. Read the value of N.
4. Calculate sum = N * (N + 1) / 2.
5. Display sum.
6. End

e) Algorithm to display the multiplication table for a given integer:

1. Start
2. Declare variables N, i.
3. Read the value of N.
4. For i = 1 to 10, display N * i.
5. End

f) Algorithm to calculate the factorial of a given number:

1. Start
2. Declare variables N, factorial.
3. Read the value of N.
4. Set factorial = 1.
5. For i = 1 to N, calculate factorial = factorial * i.
6. Display factorial.
7. End

g) Algorithm to check whether a given number is an Armstrong number or not:

1. Start
2. Declare variables N, temp, remainder, result.
3. Read the value of N.
4. Set temp = N and result = 0.
5. While temp != 0, calculate remainder = temp % 10, result = result + remainder^3, temp = temp / 10.
6. If result == N, display 'N is an Armstrong number'.
7. Else display 'N is not an Armstrong number'.
8. End

h) Algorithm to determine whether a given number is prime or not:

1. Start
2. Declare variables N, i, flag.
3. Read the value of N.
4. If N <= 1, display 'N is not a prime number'.
5. Else set flag = 0, for i = 2 to sqrt(N), if N % i == 0, set flag = 1 and break.
6. If flag == 0, display 'N is a prime number'.
7. Else display 'N is not a prime number'.
8. End