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f(x) = x^4 + x^3 - 3x^2 - 7x - 4 Find this root and then use the calculator to...

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kristenmarieb... | Student, Grade 10 | (Level 1) Valedictorian

Posted July 29, 2013 at 4:34 AM via web

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f(x) = x^4 + x^3 - 3x^2 - 7x - 4

Find this root and then use the calculator to determine any other irrational roots (rounded to 3 decimals).  Enter answers from smallest to largest.

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aruv | High School Teacher | (Level 2) Valedictorian

Posted July 29, 2013 at 9:05 AM (Answer #1)

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`f(x)=x^4+x^3-3x^2-7x-4`

Apply remainder theorem to factorize f(x).

f(-1)=0 this implies x+1 is factor of f(x)

`f(x)=x^4+x^3-3x^2-3x-4x-4`

`=x^3(x+1)-3x(x+1)-4(x+1)`

`=(x+1)(x^3-3x-4)`

we can solve

 x^3-3x-4=0 

we will get

x=2.1958,-1.0979+0.785 i,-1.0979-0.785i

Thus zeros of f(x) are

x=-1,2.196,-1.098+0.785i,-1.098-0.785i ,

two zeros are real and two are complex conjugate.

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