Question

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

Answer 1

Answer: p = 3 and q = - 4

Step-by-step explanation:

As - 4 is a root of x ^2 + px -4 = 0

If we put the value of x in given equation. Then the answer will be zero

So (-4 )^2 + p (-4) - 4 =0

16 -4p - 4 =0

12 - 4p =0

-4p = -12

p = 3

-4 is also the root of x^2 + px + q = 0

(-4)^2 + p(-4) + q =0

16 - 4p + q =0

As p = 3

16 -12 + q = 0

4 + q = 0

q = -4

Answer 2

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

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

ACCORDING TO QUESTION

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

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

$\alpha \beta = q$

$from \: eq(ii)$

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

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

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

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