How do you find the zeros, real and imaginary, of #y= -x^2-2x-1 # using the quadratic formula?

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Answer 1 · 2016-12-26T20:18:16

There are a double rooth, x = - 1.

Applying the Quadratic Formula, we can obtain the rooth of:

#y = - x^2 - 2 x - 1#,

solving the equation:

#- x^2 - 2 x - 1 = 0#.

Remember the Quadratic Formula:

When #a x^2 + b x + c = 0#, the solutions are:

#x = {- b +- sqrt {b^2 - 4 cdot a cdot c}}/{2 cdot a}#.

Applying this formula to the equation given, we have:

#x = {- (- 2) +- sqrt {(- 2)^2 - 4 cdot (- 1) cdot (- 1)}}/{2 cdot (- 1)} =#

#= {2 +- sqrt {4 - 4}}/{- 2} = - 1#.

Because the discriminant is zero, we have only one solution. In this case, the solution is real.