Find the Domain x=(-b+ square root of b^2-4ac)/(2a)

Problem

x=(−b+√(,b2−4*a*c))/(2*a)

Solution

1. Identify the constraints for a real-valued function. For the expression to be defined, the radicand (the expression inside the square root) must be non-negative, and the denominator must not be zero.

2. Set the condition for the square root. The term b2−4*a*c must be greater than or equal to zero to avoid imaginary numbers.

b2−4*a*c≥0

3. Set the condition for the denominator. The term 2*a must not equal zero to avoid division by zero.

2*a≠0

4. Solve the denominator condition for the variable a

a≠0

5. Combine the requirements to define the domain of the variables a,b, and *c The expression is defined for all real numbers such that the discriminant is non-negative and the leading coefficient is non-zero.

Final Answer

Domain: *{[(a,b,c)∈ℝ3,b2−4*a*c≥0,a≠0]}

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