Question

. If (x + a) is a factor of x 2 + px + q and x 2 + mx +n then prove that a= (n-q)/(m-q)

Answer 1

$p(x) = x {}^{2} + px + q$
$g(x) = x {}^{2} + mx + n$

given x+a is a factor of p(x) and g(x).

on puttin x = -a in p(x) and g(x) will satisfy the both equations.

$p( - a) = ( - a) {}^{2} + p( - a) + q$
$g( - a) = ( - a) {}^{2} + m( - a) + n$

$a{}^{2} - ap + q = 0$
$a {}^{2} - ma + n = 0$

$a {}^{2} = ap - q$

$a {}^{2} = ma - n$

On equating both equations above ....

ap - q = ma - n

ap - ma = q - n

a(p - m) = q - n

a = (q - n) / (p - m)

On taking - common

a = (n - q) / (m - p)


Thanks

Answer 2

Answer:

Hope this helps you ✌️✌️