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

Answer 1

Answer:

Since x= -4

Putting the value of x In the equation x2 +px-4=0

-8-4p-4=0

-4p=12

p= -4

Putting p= -4 and x= -4 in equation x2+px+q=0

-8+16+q=0

q= -8

Answer 2

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

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

ACCORDING TO QUESTION

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

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

$\alpha \beta = q$

$from \: eq(ii)$

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

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

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

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