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anonymous
 one year ago
I have been told that two roots of the equation x^4  5x^2+2x=0 are 0 and 2. It then asks me to find the two other roots. The method I have been given tells me to use the constant and check all the factors of the constant with the equation to find the roots. Since there is no constant, will you please help me find what to do?
anonymous
 one year ago
I have been told that two roots of the equation x^4  5x^2+2x=0 are 0 and 2. It then asks me to find the two other roots. The method I have been given tells me to use the constant and check all the factors of the constant with the equation to find the roots. Since there is no constant, will you please help me find what to do?

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triciaal
 one year ago
Best ResponseYou've already chosen the best response.0if the roots are a and b then (xa) and (xb) are factors of the polynomial. the highest exponent of the variable is 4 so there are 4 roots. f(x) = (xa)(xb)(xc)(xd) roots a, b, c, d f(x) divided by (xa)(xb) = (xc)(xd)

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0can you see f(x)/x(x+2) = a quadratic to be factored ? when you factor that quadratic set = 0 solve to get the other roots

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440434498406:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, I divided x^45x^2+2x by x2. I got x^3+2xx. Is that what I was supposed to do?

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0root 2 factor (x(2) = x + 2 divide yes but by x +2 other factor x

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440435257993:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When I divide the original equation by x+2 I get a remainder. Have I just made a mistake somewhere? I will send a photo of my working out...

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0sorry I am blanking out what happens when you divide by x^2 + 2 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh! I havnt done that yet! Sorry let me try that now

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0you divide the quotient by x your constant was 8 factors of 8 are ? did not check your division remainder needed for "quadratic"

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0the remainder theorem says if (xa) is a factor then there is no remainder when you compute f(a)

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440436446253:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, I know that. I just dont understand how to get the other two roots. When trying to figure out how to do it myself I looked at the answers (back of my text book) and it said the answers were 1 and plus or minus the square root of 2. How do I get to those answers? Would it be better if I sent a picture of the questions from the actual book?

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440436497477:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0sorry I can't explain it better right now when I divide f(x) by x^2 had to add 1 to complete the quadratic so x1 is a factor Quotient x^2  4 the factors are (x+2)(x2)

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0I guess from the method you need to use the remainder you have is 8 and one root is 2 so the other 4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, thanks very much for your help, unfortunately I still dont understand but maybe its because where I am its quite late so I will look at it again in the morning when you brain is fresh :). Thank you very much though
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