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solve the equation 20x^3 +44x^2 -17x -5 given that -5/2 is a zero of f(x) 20x^3 +44x^2 -17x -5

I used synthetic division and got 20x^2-6x-2=0

took 2 and divided it out of that equation

2(x+5/2)=10x^2 -3x-1
then i factored it out the right side of the equation

(x+5/2)=(5x+1)(2x-1)

then i solved for x on each and got

-5/2, -1/5, 1/2

is this correct?

  • Math -

    since x = -5/2 , one of the factors had to be (2x+5)

    when you divide f(x) by 2x+5 you get

    10x^2 - 3x - 1, not 20x^2 - 6x - 2

    I know that when you set your answer of

    20x^2 - 6x - 2 = 0 you get the same as my result when I set it mine to zero.

    You have to be careful when using synthetic division by dividing polynomials by factors of the form ax ± b
    it is safer to use long division for that.

    you then make the statement
    (x+5/2)=(5x+1)(2x-1)

    that is just wrong, they are not "equal"

    what you have to say is
    20x^3 +44x^2 -17x -5 = 0
    (2x+5)(10x^2 - 3x - 1) = 0
    (2x+5)(5x+1)(2x-1) = 0
    then x = -5/2 , we knew that, or
    x = -1/5 or x = 1/2

    I know you had those answers, but with me you would lose marks for bad form in the solution.

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