Question

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

Answer 1

Answer:

Step-by-step explanation:

(x-a)(x - b) - k = 0

x²-(a+b)x-ab-k=0

c,d are the roots then

c+d=(a+b) and cd=-ab-k

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(x-c)(x-d)+k=0

x²-(c+d)x+cd+k=0

Puttiung c+d=a+b and cd=-ab-k

x2-(a+b)+(-ab-k)+k=0

x2-ax-bx-ab-k+k=0

x2-ax-bx-ab=0

x(x-a)-b(x-a)=0

(x-a)x-b)=0

So the roots are a and b

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

hence proved