Question

If are the zeros of the polynomial p(x) = 6x3 + 3x2 - 5x +1, find the value of 1/a+1/b+1/7

Answer 1

Answer:

formula states that the sum of the three individual roots, α , β , and γ , of the cubic polynomial

f(x)=ax3+bx2+cx+d(1)

is given by the following

α+β+γ=−ba(2)

The sum of the roots pairwise is given by

αβ+αγ+βγ=ca(3)

And the product of the roots is given by

αβγ=−da(4)

I am going to assume the question is asking about the cubic

6x3+3x2−5x+1=0(5)

We are asked to find the value of

1α+1β+1γ(6)

Now we need to get this into a form easily evaluated by Vieta’s Formula. To do this we multiply creatively by the number one. (e.g., αα )

1α+1β+1γ=1α(βγβγ)+1β(αγαγ)+1γ(αβαβ)=βγαβγ+αγαβγ+αβαβγ=αβ+αγ+βγαβγ=(c/a)−(d/a)=−cd=−−51=5(7)