First slide

Theory of equations

Question

If c, d are the roots of the equation (x – a) (x – b) – k = 0, then the roots of the equation (x – c) (x – d) + k = 0 are

Moderate

A

c,d
B

a,c
C

b,d
D

a,b

Solution

we have,
$\Rightarrow x^{2} - (a + b) x + ab - k = 0$
$\Rightarrow x^{2} - (a + b) x + ab - k = 0 - - - - (1)$
Since the roots of Eq. (1) are c and d
$\begin{aligned} ∴ c + d & = a + b, - - - - (2) \\ and cd & = ab - k - - - (3) \\ Now, (x - c) (x - d) + k & = 0 \\ \Rightarrow x^{2} - (c + d) x + cd + k & = 0 \\ \Rightarrow x^{2} - (a + b) x + ab & = 0 \end{aligned}$
[Putting the values of a + b and ab from Eqs (2) and (3)]
$\Rightarrow (x - a) (x - b) = 0 \Rightarrow x = a, b$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App