Question

if alpha and beta are the zeros of polynomial p(x)= 6x^3 + 3x^2 - 5x + 1 find the value of (1/alpha + 1/beta + 1/gamma)

Answer 1

As We know that α, β are the zeroes of the polynomial 6x³ + 3x² - 5x + 1.

Let the third Zeroes of the polynomial be γ.

As We know the different relations b/w the Zeroes of the polynomials.

→ α+β+γ = -b/a

→ α+β+γ = -3/6

→ α+β+γ = -½

→ αβ+βγ+γα = c/a

→ αβ+βγ+γα = -5/6

→ αβγ = – d/a

→ αβγ = –1/6

Finally, It's time to find the suitable value of Desired problem.

→ 1/α + 1/β + 1/γ

→ (βγ+γα+αβ)/αβγ

→ ( –5/6)/(–1/6)

→ –5/–1

→ 5

Hence,

The value of 1/alpha + 1/beta + 1/gamma is 5.