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:

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

Answer 2

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

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

ACCORDING TO QUESTION

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

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

$\alpha \beta = q$

$from \: eq(ii)$

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

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

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

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