Solve using quadratic methods x4 8x2 15 0Solutiongiven x4

Solve using quadratic methods: x^4 - 8x^2 + 15 = 0

Solution

given

x^4 -8x^2 +15 =0

plug x= sqrt(3)

then we get

[sqrt(3) ]^4 - 8[sqrt(3)]^2 +15=0

9 - 8(3) +15=0

24 -24=0

0 =0

so sqrt(3) is a root of (x^4 -8x^2 +15 =0)

similerly if we plug x= -sqrt(3) also we get 0 =0

so sqrt(3) and -sqr(3) are roots of x^4 -8x^2 +15=0

so can be written as (x^2-3) (x^2 -5)

so (x^2 -3) (x^2 -5) =0

so roots are -sqrt(3) , sqrt(3) , sqrt(5) and -sqrt(5)

x^4 -8x^2 +15 =0 can be written as

[x- sqrt(3) ] [ x+ sqrt(3) ] [x -sqrt(5) ] [x +sqrt(5) ]=0