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Math Help - Quadratic equation

  1. #1
    Newbie magaski's Avatar
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    Smile Quadratic equation

    1)For what value of a,quadratic equation x^2(a^2-5a+6)+x(a^2-3a+2)+a^2-4 =0 will have more than two roots.


    2)if the equation x^2(a^2+a-2)+x(a^2+m-3)+(a^2-1)=0 is satisfied by more than two values of x. find the values of a and m.


    MENTION ALL THE STEPS .
    Last edited by magaski; January 17th 2010 at 09:37 AM.
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by magaski View Post
    1)For what value of a,quadratic equation x^2(a^2-5a+6)+x(a^2-3a+2)+a^2-4 =0 will have more than two values of x.


    2)if the equation x^2(a^2+a-2)+x(a^2+m-3)+(a^2-1)=0 is satisfied by more than two values of x. find the values of a and m.


    MENTION ALL THE STEPS .
    I don't get what you mean by "more than two values of x". By my understanding quadratics only have two roots (ie: cross the x axis). These can be real and different, real and equal or complex
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  3. #3
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    Quote Originally Posted by magaski View Post
    1)For what value of a,quadratic equation x^2(a^2-5a+6)+x(a^2-3a+2)+a^2-4 =0 will have more than two roots.
    Normally, a quadatic (the coefficient of x^2 not equal to 0) will have two roots and a linear equation (the coefficient of x^2 equal to 0 but the coefficient of x not equal to 0) will have 1. This will have an infinite number of solutions only if a^2- 5a+ 6= 0, a^2- 3a+ 2= 0 and a^2- 4= 0. What is a common factor of all of those?


    2)if the equation x^2(a^2+a-2)+x(a^2+m-3)+(a^2-1)=0 is satisfied by more than two values of x. find the values of a and m.
    Same thing: for what values of m do a^2+ a- 2, a^2+ m- 2= 0, and a^2- a have a common factor and what is that common factor?


    MENTION ALL THE STEPS .
    Since this is your exercise, why don't you at least try before asking someone to do it for you?
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  4. #4
    Newbie magaski's Avatar
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    I had tried these questions,but I didnot get the answer. Please help me in solving these problems.
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  5. #5
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    The only way I can think of for you to have more than 2 x intercepts in either case is to have a be a function of x...
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  6. #6
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    Quote Originally Posted by magaski View Post
    I had tried these questions,but I didnot get the answer. Please help me in solving these problems.
    Apparently you have NOT tried doing exactly what I told you to do: "This will have an infinite number of solutions only if a^2- 5a+ 6= 0<br />
, a^2- 3a+ 2= 0 and a^2- 4= 0. What is a common factor of all of those?" For what value of a will all of those be 0?
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  7. #7
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    Quote Originally Posted by Prove It View Post
    The only way I can think of for you to have more than 2 x intercepts in either case is to have a be a function of x...
    No. This problem will have an infinite number of solutions (in fact, every real number will be a solution) for a single value of a.
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  8. #8
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    Post Hint.

    For this quadratic eqn to have more than two roots,this quadratic eqn. must be an identity. Is my statement correct?
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