Question

If the roots of the equation $(x-a)(x-b)-k=0$ be $c$ and $d,$ then prove that the roots of the equation $(x-c)(x-d)+k=0$ are $a$ and $b.$

Answer 1

According to the question,
$(x-a)(x-b)-k\equiv (x-c)(x-d)$
or $(x-c)(x-d)+k\equiv (x-a)(x-b)$

This relation shows that the roots of $(x-c)(x-d)+k=0$ are $a$ and $b$

Hence, Proved.