Question

If a, ß, y are the zeroes of the polynomial ax3 + bx?
+ cx + d, a = 0, then the value of a2 + 32 + y2 is​

Answer 1

• α,β and γ are the Zeroes of the polynomial ax³ + bx² + cd + d ,a≠0.

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

→ α+β+γ = –b/a

→ αβ+βγ+γα = c/a

→ (α+β+γ)² = α²+β²+γ²+2(αβ+βγ+γα)

→ (–b/a)² = α²+β²+γ²+2(c/a)

→ b²/a² = α²+β²+γ²+(2c/a)

→ b²/a² – 2c/a = α²+β²+γ²

→ (b²–2ac)/a² = α²+β²+γ²

Hence,

The value of the α²+β²+γ² is (b²–2ac)/a².