How do you find all the zeros of #P(x) = x^4 − 26x^2 + 25 #?

1 Answer

Answer:

#x=+-1# and #x=+-5#

Explanation:

to find the zeros of #P(x)=x^4-26x^2+25#, set #P(x)=0#

it becomes #x^4-26x^2+25=0#

Solve by factoring because it is factorable!

#x^4-26x^2+25=0#

#(x^2-1)(x^2-25)=0#
set both factors to zero

#(x^2-1)=0# and #(x^2-25)=0#
solve for x:

#x=-1# and #x=+1#, and #x=-5# and #x=+5#

God bless you...I hope the explanation helps...