Question

number of real roots of x^4-x^3-2x-4=0

Answer 1

Step-by-step explanation:

Factor $\tt {x}^{4}-{x}^{3}-2x-4$ using Polynomial Division.

$\tt \red{ \implies\tt({x}^{3}-2{x}^{2}+2x-4)(x+1)=0}$

Factor out common terms in the first two terms, then in the last two terms.

$\tt \red{ \implies\tt[{x}^{2}(x-2)+2(x-2)](x+1)=0}$

Factor out the common term x-2.

$\red{ \tt\implies(x-2)({x}^{2}+2)(x+1)=0}$

Ask: When will $\tt (x-2)({x}^{2}+2)(x+1)$ equal zero?

When x−2=0, $\tt {x}^{2}+2=0$, or x+1=0

Solve each of the 3 equations above.

$\tt x=2,-1,\pm \sqrt{2}\imath$