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Answer:
x1 = -½
x2 = -2
x3 = 3
Step-by-step explanation:
replace f (x) with 0: 0=2x³-x²-13x-6
moves the expression to the first member:
-2x³+x²+13x+6=0
rewrite the x² and 13x as a sum:
-2x³-x²+2x+x+12x+6=0
now pick up -x² from the expression:
-x²(2x+1)+2x²+x+12x+6=0
now pick up the x:
-x²(2x+1)+x(2x+1)+12x+6=0
now pick up 6:
-x²(2x+1)+x(2x+1)+6(2x+1)=0
finally pick up 2x + 1 and rewrite the x as a difference:
-(2x+1)(x²+2x-3x-6)=0 (+2x-3x is the x rewritten as the difference)
pick up x and -3:
-(2x+1)•[x(x+2)-3(x+2)]=0
pick up x + 2 and change the sign:
(2x+1)(x+2)(x-3)=0
now having this, we can solve the equations in x:
2x+1=0 ---> x=-½
x+2=0 ---> x=-2
x-3=0 ---> x=3
here are the three solutions:
x1 = -½
x2 = -2
x3 = 3