Question

If the sum of the squares of the roots of x2+px-3=0 is 10 then p

Answer 1

Step-by-step explanation:

Hi,

X² + PX - 3 = 0

Here,

a = 1 , b = p and c = -3

Sum of zeroes = -b/a

10 = -p/1

-p = 10

p = -10

Hope it will help you :)

Answer 2

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

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

ACCORDING TO QUESTION

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

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

$\alpha \beta = q$

$from \: eq(ii)$

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

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

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

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