Question

sum of the two zeros of the polynomial of degree 4 is -1 and their product is -2. If other two zeroes are root 3 and -root3. Find the polynomial

Answer 1

let the two zeroes of the fourth degree polynomial be a and b
a + b = -1 and ab = -2
(a - b)^2 = (a + b)^2 - 4ab
(a - b)^2 =9
a- b = 3
a = 1 and b= -2
sum of the zeroes = 2 - √3
sum of the zeroes (taken two at a time) =
-4(2 + √3)
sum of the zeroes (taken three at a time) =
-3(2 - √3)
product of the roots= 6√3
so the required polynomial is
x^4 - (2- √3)x^3 - 4(2+ √3)x^2 + 3(2- √3)x + 6√3

Hope it Helps!!!!!