Math, asked by ingenious, 1 year ago

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

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Answered by Kanupriya07
11
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Answered by Anonymous
0

 {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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