Answer:
x = 2 + √-16 [ (-2)⁻¹]
See steps below.
Step-by-step explanation:
Finding the zeroes of a function simply means solving for the unknown variable (in this case "x") when the function is equated to zero.
The function here is [tex]f(x) = -(x + 1)^{2} - 4 = 0[/tex]
Start by opening the bracket. Ignore the minus sign. It will be reintroduced at the end of this step.
(x + 1)(x + 1) = x² + x + x + 1 = x² + 2x + 1
Reintroduce the minus sign. Don't forget to put the result above back in a bracket.
- (x² + 2x + 1) = -x² -2x -1
Place the expression back in the equation and solve. Make sure to put it back in the position where it was.
-x² - 2x - 1 - 4 = 0
Simplify the non-algebraic terms.
-x² - 2x - 5 = 0
Use Quadratic Formula to solve for x.
Quadratic formula: x = -b ± √(b² - 4ac)
2a
a = the coefficient of x² = -1
b = the coefficient of x = -2
c = the unit term = -5
So x = -(-2) ± √ [(-2)² - 4(-1 x -5)]
2(-1)
x = 2 + √-16 or x = 2 - √-16
-2 -2
This is where the evaluation ends, since the square root of minus sixteen cannot be evaluated. x hence is equal to a complex number. The above are the two values for x.
Next step is to put it in "a + bi" form.
x = 2 + √-16 ÷ -2 = 2 + √-16 x (-2)⁻¹
So x = 2 + √-16 [ (-2)⁻¹]
where
a is 2;
b is √-16
i is [(-2)⁻¹]
