SOLUTION: Find the exact value of the sum of the reciprocal of the roots of the equation 3x^2-4x-5=0

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Question 939564: Find the exact value of the sum of the reciprocal of the roots of the equation 3x^2-4x-5=0
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Find the roots.
Find the sum of them.

%284%2B-+sqrt%2816%2B4%2A3%2A5%29%29%2F%282%2A3%29

%284%2B-+sqrt%2816%2B60%29%29%2F6

%284%2B-+sqrt%2876%29%29%2F6

%284%2B-+2sqrt%2819%29%29%2F6

%282%2B-+sqrt%2819%29%29%2F3

----

%282-sqrt%2819%29%2B2%2Bsqrt%2819%29%29%2F3

highlight%284%2F3%29

NOTE: You can derive a formula for the question generally!

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value of the sum of the reciprocal of the roots of the equation 3x^2-4x-5=0


x+=+%28-+b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29

With a being 3; b being - 4; and c being - 5, we get:

x+=+%28-+-+4+%2B-+sqrt%28%28-+4%29%5E2+-+4%283%29%28-+5%29%29%29%2F%282%283%29%29______x+=+%284+%2B-+sqrt%2816+%2B+60%29%29%2F6______x+=+%284+%2B-+sqrt%2876%29%29%2F6

x+=+%284+%2B-+sqrt%284+%2A+19%29%29%2F6______x+=+%284+%2B-+2sqrt%2819%29%29%2F6______x+=+2%282+%2B-+sqrt%2819%29%29%2F6______x+=+cross%282%29%282+%2B-+sqrt%2819%29%29%2F3cross%286%29%29



Exact root 1: %282+%2B+sqrt%2819%29%29%2F3, and exact root 1's reciprocal: 3%2F%282+%2B+sqrt%2819%29%29



Exact root 2: %282+-+sqrt%2819%29%29%2F3, and exact root 2's reciprocal: 3%2F%282+-+sqrt%2819%29%29

Sum of exact roots' reciprocals: %283%2F%282+%2B+sqrt%2819%29%29+%2B+3%2F%282+-+sqrt%2819%29%29%29

 -------- Multiplying by LCD, %282+%2B+sqrt%2819%29%29%282+-+sqrt%2819%29%29 

_____12%2F%282+%2B+sqrt%2819%29%29%282+-+sqrt%2819%29%29______12%2F%284+-+19%29______12%2F%28-+15%29______4cross%2812%29%2F%28-+5cross%2815%29%29

Exact value of sum of exact roots' reciprocals: highlight_green%28-+4%2F5%29