The number of distinct real roots of the equation x 5( x 3- x 2- x +1)+ x (3 x 3-4 x 2-2 x +4)-1=0 text is

Question

The number of distinct real roots of the equation x 5( x 3- x 2- x +1)+ x (3 x 3-4 x 2-2 x +4)-1=0 text is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

x5(x3-x2-x+1)+x(3 x3-4 x2-2 x+4)-1 =0 ⇒(x-1)2(x+1)(x5+3 x-1)=0 Let f(x)=x5+3 x-1 f prime(x)>0 ∀ x ∈ R Hence 3 real distinct roots.

Q. The number of distinct real roots of the equation
$x^{5} (x^{3} - x^{2} - x + 1) + x (3 x^{3} - 4 x^{2} - 2 x + 4) - 1 = 0 is$