## anonymous 5 years ago determine an equation in simplified form for the family of quartic functions with zeros -1-√5 and -1+√5 and 2+√2 and 2-√2

1. anonymous

r u getting any help?

2. anonymous

We first find a quadratic equation with $-1-\sqrt{5}$ and $-1+\sqrt{5}$ as roots. We find the sum and product of the roots. Sum of roots: - 2 Product of roots: - 4 Now, we reverse the sign of the sum of the roots. That is 2. The equation is $x^2 +2x-4=0$. For the second quadratic equation. The equation must have $2+\sqrt2$ and $2-\sqrt2$ as roots. Sum of roots: 4 Product of roots: 2 Again, invert the sign of the sum of roots. That is - 4. The equation is $x^2 -4x+2=0$. Multiply: $(x^2 + 2x - 4)(x^2 -4x + 2) = 0$. Then, the result is your final answer. Hope this helps a lot :)