Answer :
Answer:
The zeroes of the given equation are x = √2 , -√2 , 2 , -2.
Step-by-step explanation:
The given quadratic equation is y = [tex]x^{4}- 6x^{2}+8[/tex]
To find the zeroes , put y = 0.
[tex]x^{4}- 6x^{2}+8[/tex] = 0
Put [tex]x^{2}[/tex]=t
The new equation is [tex]t^{2} -6t +8=0[/tex]
On factorising ,
[tex](t - 4)\times(t - 2)=0[/tex]
Hence t = 2 or t = 4
On resubstituting the value of t in terms of x ,
[tex]x^{2}[/tex] = 2 or [tex]x^{2}[/tex] = 4
Taking square root of above equation , we get
x = √2,-√2,2,-2
These are the 4 roots of the given equation .