Question

How do I find all the real zeros of the polynomial function of these 3 ? ):

1) g(t) = 1/2t^4-1/2
2) g(t) = t^5-6t^3+9t
3) f(x) = 5x^4+15x^2+10

Answer 1

1. take out a common factor of 1/2, then factor as a difference of squares
(1/2)(t^2 + 1)(t-1)(t+1)
etc

2.
t(t^4 - 6t^2 + 9)
= t(t^2 - 3)(t^2 -3)
etc

3. 5(x^4 + 3x^2 + 2)
= 5(x^2 + 1)(x^2 + 2)
etc