Answer-
2 is the upper limit for the zeros.
Solution-
The given function f(x) is,
[tex]2x^4 -7x^3 + 4x^2 + 7x - 6 = 0[/tex]
For calculating the zeros,
[tex]\Rightarrow f(x)=0[/tex]
[tex]\Rightarrow 2x^4 -7x^3 + 4x^2 + 7x - 6 = 0[/tex]
[tex]\Rightarrow 2x^4-4x^3-3x^3+6x^2-2x^2+ 4x+3x-6=0[/tex]
[tex]\Rightarrow 2x^3(x-2)-3x^2(x-2)-2x(x-2)+3(x-2)=0[/tex]
[tex]\Rightarrow (x-2)(2x^3-3x^2-2x+3)=0[/tex]
[tex]\Rightarrow (x-2)(x^2(2x-3)-1(2x-3))=0[/tex]
[tex]\Rightarrow (x-2)(x^2-1)(2x-3)=0[/tex]
[tex]\Rightarrow (x-2)(x+1)(x-1)(2x-3)=0[/tex]
[tex]\Rightarrow x-2=0,\ x+1=0,\ x-1=0,\ 2x-3=0[/tex]
[tex]\Rightarrow x=2,\ x=-1,\ x=1,\ x=\frac{3}{2}[/tex]
From all the 4 roots, it can be obtained that 2 is the greatest zero.
