Find all real zeros of the function. f(x)=4x^4-8x^3-19x^2+23x-6

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rcmath | High School Teacher | (Level 1) Associate Educator

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We are going to factor the polynomial.

I am going to use long division to do that. Let's try to divide by x+2

`4x^3-16x^2+13x-3`

x+2   `4x^4-8x^3-19x^2+23x-6`

`4x^4+8x^3`

`-16x^3-19x^2`

`-16x^3-32x^2`

`13x^2+23x``

`13x^2+26x`

`-3x-6`

In a similar manner we can try to divide our quotient by let's say x-3

So I obtain `(x+2)(x-3)(4x^2-4x+1)=(x+2)(x-3)(2x-1)^2`

To obtain the zeros we set our function to equal zero, thus

either x+2=0, x-3=0, or 2x-1=0.

Hence the zeros are x=-2, x=3, or x=1/2

 

 

 

 

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