Answer :
Answer:
The equation which has exactly two real and non-real solutions is:
C: x^4-5x^2-36=0
Step-by-step explanation:
x^4-5x^2-36=0 (given equation)
By Factorization:
x^4-9x^2+4x^2-36=0 .... (1) (Mid term break rule)
as, (-5x^2)=(-9x^2+4x^2)
and 36 =9*4
x^2(x^2 - 9) +4(x^2 - 9)=0
taking like terms common from (1)
(x^2+4) (x^2 - 9)=0
we have:
x^2 - 9=0 and x^2 + 4=0
x^2=-9 x^2= -4
Taking square root on both sides
x= (+3, -3) and x=(+2i, -2i ) (here [i=iota=[/tex] \sqrt(-1)\\[/tex])
hence,
x=(+3, -3) are real roots of given equation.
x=(+2i, -2i) are non-real roots of given equation.