Find the roots of x^4 – 13x^2 + 36 = 0

We have to find the roots of x^4 – 13x^2 + 36 = 0. As we have x
raised to the power 4, we are going to have 4 roots.

Now let us see
the given equation :

x^4 – 13x^2 + 36 =
0

we see that -13 can be written as -4 – 9 so that the sum is -13
and the product is 36

=> x^4 – 4x^2 – 9x^2 + 36 =
0

=> x^2 ( x^2 – 4) – 9( x^2 – 4) =
0

=> (x^2 – 4)(x^2 – 9) =0

Now
x^2 – 4 and x^2 – 9 can be factorized using the relation x^2 – y^2 = (x – y)*(x +
y)

=> (x – 2)(x + 2)(x – 3)(x + 3)
=0

So for (x – 2) = 0, we have x =
2

for (x + 2) = 0, we have x = -2

for
(x – 3) = 0 we have x = 3

and for (x + 3) =0, we have x =
-3

Therefore the roots of x^4 – 13x^2 + 36 = 0 are x =
2, x = -2, x = 3 and x = -3.