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

Question

2732 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-05T15:14:52

Form a quadratic equation, and solve it. Method below first, solution underneath.

Method

Start by writing your equation in the form:
#y=ax^2+bx+c#

The roots are when #y=0#
So you will have a quadratic equation of the form:
#ax^2+bx+c=0#

#x=(-bpmsqrt(b^2-4ac))/(2a)#

Which can give two roots due to the #pm#square root.

Solution

#y=-x^2+0x+2#

for roots, #y=0#

#-x^2+0x+2=0#

#a=-1, b=0, c=2#

so

#x=(pmsqrt(8))/(-2)=pmsqrt2#

#x=sqrt2#

or

#x=-sqrt2#