Question

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

Answer 1

Answer:

Step-by-step explanation:

α and β are roots, then equation is (x -α)(x -β)=0

so,if c and d are roots, then equation will be  (x -c)(x -d)=0

but,here c and d are roots of the equation (x -a)(x -b) -k =0

so, (x -c)(x -d)= (x -a)(x -b) -k 

⇒(x -c)(x -d) + k = (x -a)(x -b)_______(1)

∵  a and b are roots of equation (x -a)(x -b)=0 

and from equation (1) 

(x -c)(x -d) + k = (x -a)(x -b)

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

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