Question

Boundary points are 1,-1,6, and -6 . Divid the w axis into intervals defined by the Boundary points the derermain the sign of f(w). W=-7,-5,0,2,7. F(-7)=? F(-5)=? F(0)=? F(2)=? F(7)=?

Answer 1

The polynomial inequality is not described

Suppose it is;

$f(w)=x^4-37x^2+36\ge0$

Factorizing, $(x^2-1)(x^2-36)\ge0$

$\begin{matrix} \>&-7&-6&-5&-1&0&1&2&6&7 \\x^2-1 &+&&+&&-&&+&&+\\ x^2-36&+&&-&&-&&-&&+\\ sign\>of\>f(w)&+&&-&&+&&-&&+ \end{matrix}$

Solution $(-\infin,-6\>]U\>[\>-1,1\>]U\>[\>6,\infin)$