Question

Form a quadratic polynomial, one of whose zeroes are 2 + 5 and the sum of zeroes is 4.

Answer 1

given :Sum of the zeroes 4           one of the zero is 2+√5==αanother zero is 2-√5==β because 2+√5+β=4                                    β=4-2+√5                                    β=2-√5So here in order to get the equation we need substitute in general formula of quadratic equationx²-(α+β)+αbx²-(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