Question

factors of x^6+14x^3-1

Answer 1

Given expression is x^6+14x^3-1

= (x^3)^2+14x^3-1

Compare it to qudratic form ax^2+bx+c

Roots are x = -b±√(b^2-4ac)

Here x = x^3

a = 1, b = 14, c = -1

x^3 = [-14±√(196+4)]/2

= [-14±√200]/2

= [-14±√100*2]/2

= 2[-7±5√2]/2

= -7±5√2

Roots are x^3 = -7+5√2 and x^3 = -7-5√2

x^6+14x^3-1 = (x^3-(-7+5√2))(x^3-(-7-5√2))

Factors of x^6+14x^3-1 is (x^3+7-5√2)(x^3+7+5√2)

 

Comments

Typo mistake in 4 th line of solution  x = [-b±√(b^2-4ac)]/2a.