Question

$x^6-26x^3-27=0$

• A. -1, 27
• B. 1, -27
• C. -1, 3
• D. 1, -3
• E. 1, 27

Answer 1

The correct option is C -1, 3

Soln:

Let$x^3=y$

$y^2-26y-27=0$

$y^2-27y+y-27=0$

$y(y-27)+1(y-27)=0$

$(y+1)(y-27)=0$

The roots are y = -1, y = 27

$x^3=-1,x=-1$

$x^3=27,x=3$

Hence option (c)

2nd method:- By observation, we can find quickly that one root will be 1 or -1, based on that choice 1 or 3 can be. For second root, it can be 3 cannot be 27.