rose8666 rose8666

06-11-2020
Mathematics

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proof that ,if the sum of the reciprocals of the roots of the equation ax^2+bx+c is 1, then b+c=0

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oscar236 oscar236

06-11-2020

Answer:

Below.

Step-by-step explanation:

The sum of the roots ( A AND B) = -b/a and the product = c/a.

If the roots are A and B then 1/A + 1/B = 1

So (A + B) / AB = 1

Substituting:

-b/a / c/a = 1

-b/a * a/c = 1

= -b/c = 1

- b = c

b + c = 0.

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