Question

Find all the zeros of the function. Y=x^4 -6x^2 +8

Answer 1

Answer:

The zeroes of the given equation are x = √2 , -√2 , 2 , -2.

Step-by-step explanation:

The given quadratic equation is y = $x^{4}- 6x^{2}+8$

To find the zeroes , put y = 0.

$x^{4}- 6x^{2}+8$ = 0

Put $x^{2}$=t

The new equation is $t^{2} -6t +8=0$

On factorising ,

$(t - 4)\times(t - 2)=0$

Hence t = 2 or t = 4

On resubstituting the value of t in terms of x ,

$x^{2}$ = 2 or $x^{2}$ = 4

Taking square root of above equation , we get

x = √2,-√2,2,-2

These are the 4 roots of the given equation .