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Math Help - Synthetic division (Finding all zeros)

  1. #1
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    Synthetic division (Finding all zeros)

    Show that the given value of c is a zero of P(x), and find all other zeros of P(x) (Enter NONE in any unused answer blanks.)

    P(x) = -2x3 + 2x2 + 4x - 4, c = 1.

    I figured that all out, and 1 does bring a remainder of 0.

    And I believe my end equation is (x-1) (-2x^2+4)

    From there, I don't know how to find the other zeros... and my book doesn't help at all.

    Thanks guy
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  2. #2
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    Quote Originally Posted by shiznid12 View Post
    Show that the given value of c is a zero of P(x), and find all other zeros of P(x) (Enter NONE in any unused answer blanks.)

    P(x) = -2x3 + 2x2 + 4x - 4, c = 1.

    I figured that all out, and 1 does bring a remainder of 0.

    And I believe my end equation is (x-1) (-2x^2+4)

    From there, I don't know how to find the other zeros... and my book doesn't help at all.

    Thanks guy
    Hi shiznid12,

    p(x) = -2x^3 + 2x^2 + 4x - 4

    Your depressed polynomial is correct.

    p(x)=(-2x^2+4)(x-1)

    Factor a -2 from the first term.

    p(x)=-2(x^2-2)(x-1)

    Set p(x) =0. Evaluate x^2-2=0 to find your other two zeros.
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  3. #3
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    Quote Originally Posted by shiznid12 View Post
    Show that the given value of c is a zero of P(x), and find all other zeros of P(x) (Enter NONE in any unused answer blanks.)

    P(x) = -2x3 + 2x2 + 4x - 4, c = 1.

    I figured that all out, and 1 does bring a remainder of 0.

    And I believe my end equation is (x-1) (-2x^2+4)

    From there, I don't know how to find the other zeros... and my book doesn't help at all.

    Thanks guy
    Looks right to me. Personally I would factor out a -2 (like masters did) and use the difference of two squares:

    P(x) = -2(x-1)(x-\sqrt{2})(x+\sqrt{2})
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  4. #4
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    Wow... it's always the tiny steps that ruin everything. I didn't even think to factor out the 2

    Thanks a lot guys.
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  5. #5
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    Quote Originally Posted by shiznid12 View Post
    Wow... it's always the tiny steps that ruin everything. I didn't even think to factor out the 2

    Thanks a lot guys.
    You don't have to factor the 2, it would have came out when solving 4-2x^2=0, it just helps xD

    I'm not sure if you know but for ab=0 either a and/or b must be 0
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  6. #6
    A riddle wrapped in an enigma
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    Quote Originally Posted by shiznid12 View Post
    Wow... it's always the tiny steps that ruin everything. I didn't even think to factor out the 2

    Thanks a lot guys.
    You really don't have to factor out the -2 since all you're interested in are the remaining zeros.

    -2x^2+4=0

    -2x^2=-4

    x^2=2

    x=\pm \sqrt{2}





    Sorry to be redundant, but posted a tad too late. Yeah, what he said!
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  7. #7
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    Well it helped.

    Also... I know what I did wrong. I had 2x^2-2 = 0 on my paper instead of 4.. so I ended up with x^2=1

    I need to learn to look over my answers better
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