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 restrictions for a real-valued function, which require that the denominator is non-zero and the radicand (the expression under the square root) is non-negative.

2. Set the condition for the square root such that the radicand is greater than or equal to zero.

b2−4*a*c≥0

3. Set the condition for the denominator such that it does not equal zero.

2*a≠0

4. Solve the denominator condition for the variable a

a≠0

5. Combine the conditions to define the domain for the variables a,b, and *c

b2≥4*a*c* and *a≠0

Final Answer

Domain:{[(a,b,c)∈ℝ3,b2−4*a*c≥0,a≠0]}

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