You visited us 68 times! Enjoying our articles? Unlock Full Access!

Relationship between Zeroes and Coefficients of a Polynomial

If α ,β ,γ ...

Question

If $α, β, γ$ are the zeroes of the cubic polynomial $x^{3} + 3 x^{2} - x - 2$ , find the values of the expressions given below:
$α + β + γ, α β + β γ + γ α$ and $α β γ$ .

Open in App

Solution

$x^{3} + 3 x^{2} - x - 2$

The expression is in the from
$a x^{3} + b x^{2} + c x + d$ ,
then
$a = 1, b = 3, c = - 1, d = - 2$

$∴ α + β + γ = \frac{- b}{a} = \frac{- 3}{1} = - 3$

$α β + β γ + γ α = \frac{c}{a} = \frac{- 1}{1} = - 1$

$α β γ = \frac{- d}{a} = \frac{- (- 2)}{1} = 2$

Suggest Corrections

Similar questions

2 x^{3} + 3 x^{2} + 5 x + 6 = 0

α, β, γ

α + β + γ, α β + β γ + γ α

α β γ

α, β, γ

a x^{3} + b x^{2} + 4 x + 7 = 0

α β + β γ + γ α =

α, β, γ

x^{3} - 2 x^{2} + q x - r

α + β = 0

2 q = r

α, β, γ

a x^{3} + b x^{2} + c x + d

α + β + γ = - \frac{b}{a}, α β + β γ + γ α = \frac{c}{a}, α β, γ = - \frac{d}{a}

α, β, γ

x^{3} + p x^{2} + q x + r = 0

α (β + γ), β (γ + α), γ (α + β)

Join BYJU'S Learning Program