Question

X^-x(p+q)+pq what are zero os of polynomial?

Answer 1

To find

zeroes of x² - (p + q)x + pq

Comparing it with the standard equation ax² + bx + c, we get

a = 1

b = - (p + q)

c = pq

Now, apply quadratic formula to obtain the zeroes of the expression.

Quadratic formula :

$\sf x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

So, here

$\sf x = \frac{-(-(p+q))\pm\sqrt{(-(p+q))^2-4(1)(pq)}}{2}\\\\x=\frac{p+q\pm\sqrt{p^2+q^2+2pq-4pq}}{2}\\\\x=\frac{p+q\pm\sqrt{p^2+q^2-2pq}}{2}\\\\x = \frac{p+q\pm\sqrt{(p-q)^2}}{2}\\\\x = \frac{p+q\pm(p-q)}{2}\\\\x = \frac{p+q+p-q}{2} \ or \ x = \frac{p+q-(p -q)}{2}\\\\x = \frac{2p}{2}\ or \ x = \frac{2q}{2}\\\\x = p\ or\ x = q$

Hence, the zeroes of given expression are p and q