Question

if p,q are the roots of
${ax}^{2} + bx + c = 0$
then find
$( \frac{1}{p} - \frac{1}{q} ) {}^{2}$
​no spams

Answer 1

Answer:

p and q are the roots of given eqn ax^2+bx+c=0

p+q=-b/a

pq=c/a

now

(1/p-1/q)^2

={q-p/pq}^2

=(q-p) ^2/(pq) ^2

=(p-q) ^2/(pq)^2

=(p+q)^2-4pq/(pq) ^2

=(-b/a)^2-4(c/a)/(c/a)^2

=b^2/a^2-4c/a/(c/a)^2

=b^2-4ac/a^2/(c/a)^2

=b^2-4ac/c^2 (ans)...