Question #49380

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Answer 1 · 2018-02-26T14:54:09

i. #k<+-1#
ii. #k=+-1#
iii. #k>+-1#

We can rearrange to get: #x^2+4-k(x^2-4)=0#

#x^2(1-k^2)+4+4k=0#

#a=1-k#
#b=0#
#c=4+4k#

The discriminant is #b^2-4ac#

#b^2-4ac=0^2-4(1-k)(4+4k)=16k^2-16#

#16k^2-16=0#

#16k^2=16#

#k^2=1#

#k=+-1#

If #k=+-1#, the discriminant will be #0#, meaning 1 real root.

If #k>+-1#, the discriminant will be #>0#, meaning two real and distinct roots.

If #k<+-1#, the discriminant will be #<0#, meaning no real roots.