Question

If alpha beta are roots of (x-c)(x-d)+k=0 then find the roots of (x-a)(x-b)-k=0​

Answer 1

Correct Question:

If 'a' and 'b' are roots of (x-c)(x-d)+k=0 then find the roots of (x-a)(x-b)-k=0

Answer:

$\bold\green{Roots}= \bold\red{c}\:\:and\:\bold\red{d}$

Step-by-step explanation:

We know that,

If μ and π are roots of quadratic equation,

$\bold{a{x}^{2}+bx+c=0}$

then,

we may write the equation as,

$\bold{a(x-μ)(x-π)=0}$

Now,

Given that,

'a' and 'b' are roots of (x-c)(x-d)+k=0

$= > (x - c)(x - d) + k = (x - a)(x - b) \\ \\ = > (x - a)( x - b) - k = (x - c)(x - d)$

Therefore,

comparing the equations,

we get,

Roots are 'c' and 'd'