Question

form a quadratic polynomial one of whose zeroes is 2+ root 5 and the sum of the zeroes is 4

Answer 1

Given :Sum of the zeroes 4
one of the zero is 2+√5==α
another zero is 2-√5==β because 2+√5+β=4
β=4-2+√5
β=2-√5
So here in order to get the equation we need substitute in general formula of quadratic equation
x²-(α+β)+αb
x²-(4)x+(2+√5.2-√5) {(a+b)(a-b)==a²-b²}
x²-4x+(4-5)
x²-4x+(-1)
x²-4x-1 is the answer