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Question: The equation $$3x^2-6x-4=0$$ has roots α and β. Find the value of 1/α + 1/β.

I'd just like confirmation on my answer, as I've already found the answer but am not confident in it.

since αβ=c/a and α+β= -b/a 1/α +1/β= (α+β)/αβ= (-b/a)/(c/a)=2/(-4/3)=-3/2

nonuser
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injustice fellow
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1 Answers1

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Yes, it is correct.

You could do also like this. You have to find $a+b$ if $a,b$ are solution to $$3{1\over x^2}-6{1\over x}-4=0$$that is $$3-6x-4x^2=0$$

so $$a+b =-{-6\over -4}=-{3\over 2}$$

nonuser
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    Quite right. One should always keep in mind that if $\sum_0^na_ix^i$ is the original polynomial, the polynomial with the reciprocals of its roots is $\sum_0^na_ix^{n-i}$. – Lubin Apr 24 '19 at 18:15