Question
Determine the values of the variable for which the expression is defined as a real number. (Enter your answer using interval notation.)
x2 − 5x − 50
x2 − 5x − 50
Answers
GPT 3.5
To determine the values of x for which the expression is defined as a real number, we need to find the values of x that make the discriminant of the quadratic equation \(x^2 -5x - 50\) nonnegative.
The discriminant is given by \(b^2 - 4ac\), where \(a = 1\), \(b = -5\), and \(c = -50\).
Substituting these values into the discriminant formula, we have \((-5)^2 - 4(1)(-50) = 25 + 200 = 225\).
Since the discriminant is positive, the quadratic equation has two distinct real roots. Therefore, the expression \(x^2 - 5x - 50\) is defined as a real number for all values of x.
Using interval notation, the values of x for which the expression is defined are \((-∞, ∞)\).
The discriminant is given by \(b^2 - 4ac\), where \(a = 1\), \(b = -5\), and \(c = -50\).
Substituting these values into the discriminant formula, we have \((-5)^2 - 4(1)(-50) = 25 + 200 = 225\).
Since the discriminant is positive, the quadratic equation has two distinct real roots. Therefore, the expression \(x^2 - 5x - 50\) is defined as a real number for all values of x.
Using interval notation, the values of x for which the expression is defined are \((-∞, ∞)\).