Question

If p and q are the roots of the equation x2-px+q=0 then

Answer 1

Given: The equation x^2 - px + q = 0

To find: The value of p?

Solution:

• Now we have given that p and q are the roots.

• The equation is x^2 - px + q = 0

• So sum of roots is p + q = p

              p - p = q

              q = 0

• Now product of roots is pq = q

              p = 1

Answer:

          So the value of p is 1 and q is 0.

Answer 2

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

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

ACCORDING TO QUESTION

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

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

$\alpha \beta = q$

$from \: eq(ii)$

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

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

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

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