If $ax^2+(b+c)x+d+e=0$ has roots greater than $1$, then show that $ax^4+bx^3+cx^2+dx+e$ has at least one real root
If $ax^2+(c+b)x+e+d=0$ has real roots greater than $1$, show that $ax^4+bx^3+cx^2+dx+e$ has at least one real root