SOLUTION: Find the sum of reciprocals of the roots to the quadratic 3x^2-4x-7=0.

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Question 998854: Find the sum of reciprocals of the roots to the quadratic 3x^2-4x-7=0.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2-4x-7=0..........factor completely
3x%5E2%2B3x-7x-7=0
%283x%5E2%2B3x%29-%287x%2B7%29=0
3x%28x%2B1%29-7%28x%2B1%29=0
%28x%2B1%29%283x-7%29+=+0
roots:
if %28x%2B1%29+=+0=>x=-1
if %283x-7%29+=+0=>x=7%2F3

reciprocal of x=-1 is x=1%2F-1=-1
reciprocal of x=7%2F3 is x=1%2F%287%2F3%29=3%2F7
their sum is:-1%2B3%2F7=-7%2F7%2B3%2F7=-4%2F7


Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.
3x%5E2+-+4x+-+7 = 0,

x%5B1%2C2%5D = %284+%2B-+sqrt%284%5E2+%2B+4%2A3%2A7%29%29%2F6 = %284+%2B-+10%29%2F6.

x%5B1%5D = 14%2F6 = 7%2F3.

x%5B2%5D = -1.

The sum of reciprocals of the roots is 3%2F7 + %28-1%29 = -4%2F7.