Find the zeros of the function algebraically. (Enter your answers as a comma-separated list.) f(x)=x3−6x2−9x+54

Question

Find the zeros of the function algebraically. (Enter your answers as a comma-separated list.)  f(x)=x3−6x2−9x+54

censoratojk · Accepted Answer

Step 1  f(x)=x3−6x2−9x+54  x3−6x2−9x+54=0  bring out common values  x2(x−6)−9(x−6)=0  (x−6)(x2−9)=0  Step 2  (x−6)(x2−32)=0  (x−6)(x−3)(x+3)=0  therefore zeros are   x=6,3,−3 answer

Dabanka4v · Accepted Answer

Explanation:   Group the terms into pairs as follows.  [x3+6x2]+[−9x−54]  Now, factorize each &quot;pair&quot;  x2(x+6)−9(x+6)  Take out the common factor of (x+6)  (x+6)(x2−9)  x2−9 is a difference of squares and in general factorises.  a2−b2=(a−b)(a+b)  x2=(x)2 and 9=(3)2⇒a=x and b=3  ⇒x2−9=(x−3)(x+3)  Pulling this altogether we get.  x3+6x2−9x−54=(x+6)(x−3)(x+3)

nick1337 · Accepted Answer

We need to find the values where the function tends to 0, so we need to make the equation, equal to 0: x3+6x2−9x−54=0 x2(x+6)−9(x+6)=0 x2−9(x+6)=0 (x+3)(x-3)(x+6)=0 Then, we have three factors multiplying each other, so we have to five three numbers which make at least one of those factors 0 So, Trying with 3: (x+3)(x-3)(x+6)=0 (3+3)(3-3)(3+6)=0 (3+3)(0)(3+6)=0 0=0 Trying with -3: (x+3)(x-3)(x+6)=(-3+3)(-3-3)(-3+6)=0 (0)(-6)(3)=0 0=0 Trying with -6: (x+3)(x-3)(x+6)=(-6+3)(-6-3)(-6+6)=0 (-3)(-9)(0)=0 0=0

Find the zeros of the function algebraically. (Enter your answers

Answered question

Answer & Explanation

New Questions in Algebra I