Question

Find a quadratic polynomial whose one zero is 2+root5​

Answer 1

Answer:

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