Question

find all roots of equation x^11-x^7+x^4-1=0​
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Answer 1

Answer:

Four solutions were found :

1. x = 1
2. x= 0.0000 - 1.0000 i
3. x= 0.0000 + 1.0000 i
4. x = -1

Step-by-step explanation:

Step 1 :

Step 1 :Checking for a perfect cube :

Step 1 :Checking for a perfect cube : 1.1 x^11-x^7+x^4-1 is not a perfect cube

Trying to factor by pulling out :

1.2 Factoring: x^11-x^7+x4-1

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: x4-1

Group 2: x11-x7

Pull out from each group separately :

Group 1: (x4-1) • (1)

Group 2: (x4-1) • (x7)

Add up the two groups :

(x4-1) • (x7+1)

Answer 2

Answer:

Solution:-

Step 1:-

Checking for a perfect Cube :-

x^11-x^7+x^4-1 is not a perfect cube.

Trying to pulling out Factor:-

Factoring :- x^11-x^7+x^4-1

Group 1 = x⁴ - 1

Group 2 = x^11 - x^7

Pull out from each group Separately:-

Group 1 = (x⁴-1) (1)

Group 2 = (x⁴-1) (x^7)

After Adding the Two Group :-

Add :- (x⁴-1) (x^7 + 1)

Hope iT Helps Uh :)