Find a polynomial Px of minimum degree with a leading coeffi

Find a polynomial, P(x), of minimum degree with a leading coefficient of 1 that has the given zeros. 0, 2i, 2+i

P(x)=________

Solution

Given :

zeroes are:

0, 2-i , 2+i

so, x(x-( 2-i) ) ( x - ( 2+i) ) = 0

= x ( x -2+i) ( x - 2 - i)

= x³ - 4x² + 5x { since i² = -1 }

Hence polynmial p(x) = x³ - 4x² + 5x [ Answer ]