Question

Find an upper limit for the zeroes 2x^4 -7x^3 + 4x^2 + 7x - 6 = 0

Answer 1

Answer-

2 is the upper limit for the zeros.

Solution-

The given function f(x) is,

$2x^4 -7x^3 + 4x^2 + 7x - 6 = 0$

For calculating the zeros,

$\Rightarrow f(x)=0$

$\Rightarrow 2x^4 -7x^3 + 4x^2 + 7x - 6 = 0$

$\Rightarrow 2x^4-4x^3-3x^3+6x^2-2x^2+ 4x+3x-6=0$

$\Rightarrow 2x^3(x-2)-3x^2(x-2)-2x(x-2)+3(x-2)=0$

$\Rightarrow (x-2)(2x^3-3x^2-2x+3)=0$

$\Rightarrow (x-2)(x^2(2x-3)-1(2x-3))=0$

$\Rightarrow (x-2)(x^2-1)(2x-3)=0$

$\Rightarrow (x-2)(x+1)(x-1)(2x-3)=0$

$\Rightarrow x-2=0,\ x+1=0,\ x-1=0,\ 2x-3=0$

$\Rightarrow x=2,\ x=-1,\ x=1,\ x=\frac{3}{2}$

From all the 4 roots, it can be obtained that 2 is the greatest zero.