Calculate the Discriminant Value
In algebra, Discriminant helps us deduce various properties of the roots of a polynomial or polynomial function without even computing them. Let’s look at this general quadratic polynomial of degree two:
ax^2+bx+c
Here the discriminant of the equation is calculated using the formula:
b^2-4ac
Now we can deduce the following properties:
- If the discriminant is equal to zero then the polynomial has equal roots i.e., a=b.
- If the discriminant is positive and the coefficients are real, then the polynomial has two real roots.
Here are a few conditions that we must keep in mind while programming and making deductions from the discriminant:
- If the discriminant is equal to zero then one solution is possible.
- If the discriminant is positive then two solutions are possible.
- If the discriminant is negative then no real solutions are possible.
Examples:
Input: a = 20 b = 30 c = 10 Explanation: (30**2) - (4*20*10) Output: Discriminant is 100 which is positive Hence Two solutions Input: a = 9 b = 7 c = 12 Explanation: (30**2) - (4*20*10) Output: Discriminant is -383 which is negative Hence no real solutions
C++
Java
Python3
C#
PHP
Javascript
Output:
Discriminant is 100 which is Positive Hence Two Solutions
Time Complexity: O(1) since constant operations are being performed
Auxiliary Space: O(1), since no extra space has been taken.
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