Question

find all the zeros of x^4 - 5x³ + x² +15x -12, if it is given that two of its zeros are 1 and 4.

Answer 1

zeroes are 1 and 4
(x-1)(x-4)are factors
$x^2-5x+4$ is a factor
on dividing,
we get quotient=$x^2-3$
=$(x- \sqrt{3})(x+ \sqrt{3})$
hence,√3 and -√3 are remaining zeroes

Answer 2

ATQ zeros are 1 and 4 therefore(x-1) and (x-4) are factor therefore x^2-5x+4 is a factor on dividing we quotient=x^2-3=(x-√3)(x+√3)