Question

Find all zeroes of the polynomial 4x^4-20x³+23x²+5x-6,if two of its zeroes are 2 and 3

Answer 1

we know the two roots of the equation

let other two be x and y

2+3+x+y = -(-20)/4=5 -----(1)

2*3*x*y=-6/4 = -3/2 ----(2)

from 1

x+y=0. => x=-y

from 2

xy=-1/4 => x^2=1/4 => x=+1/2 , -1/2

=> y=-1/2 , +1/2 (should be of opposite sign)