If -4 is a root of the equation x2+ px – 4 = 0 and the equation x2 + px +q = 0 has equal roots, find the value of p and q​

Question

If -4 is a root of the equation x2+ px – 4 = 0 and the equation x2 + px +q = 0 has equal roots, find the value of p and q​

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Julia 3 months 2021-11-02T20:59:20+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-02T21:01:14+00:00

    Answer:

    p= -3 q= -28

    Step-by-step explanation:

    since the root is given we can substitute the value in the equation

    (-4)²-4p-4=0

    on evaluating,

    p= -3

    and substituting the values into 2nd equation

    q= -28

    0
    2021-11-02T21:01:17+00:00

     {x}^{2}  + px + q = 0.....(i)

    let \alpha , \beta  \: be \: roots \: of \: eq(i)

    ACCORDING TO QUESTION

     \alpha  +  \beta  =  { \alpha }^{2}  +  { \beta }^{2} .....(ii)

    now \: term \: eq(i) \alpha  +  \beta  =  - p

     \alpha  \beta  = q

    from \: eq(ii)

     - p =  { \alpha }^{2}  +  { \beta }^{2}  = ( \alpha  +  \beta  {)}^{2}  - 2 \alpha  \beta

     - p = ( - p {)}^{2}  - 2q

     - p = {p}^{2}  - 2q

     {p}^{2}  + p - 2q = 0

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