You visited us 1 times! Enjoying our articles? Unlock Full Access!

Relationship Between Zeroes and Coefficients of a Quadratic Polynomial

If α,β and γ ...

Question

If $α, β$ and $γ$ are the zeroes of the cubic polynomial $a x^{3} + b x^{2} + c x + d$ ,
then $α + β + γ$ is equal to

$\frac{c}{a}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- $\frac{d}{a}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{c}{d}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- $\frac{b}{a}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D
- $\frac{b}{a}$

If $α, β$ and $γ$ are the zeroes of the cubic polynomial $a x^{3} + b x^{2} + c x + d$ , then

sum of its zeroes
= $α + β + γ$
= $- \frac{(c o e f f i c i e n t o f x^{2})}{(c o e f f i c i e n t o f x^{3})} = - \frac{b}{a}$

Suggest Corrections

Similar questions

If $α, β$ and $γ$ are the zeroes of the polynomial $f (x) = a x^{3} + b x^{2} + c x + d$ , then $\frac{1}{α} + \frac{1}{β} + \frac{1}{γ}$ is _____.

α, β, γ

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

= \frac{c}{a}

α, β, γ

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

α β γ =

α, β

γ

P (x) = a x^{3} + b x^{2} + c x + d, (a \neq 0)

[α . β . γ] =

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}

Join BYJU'S Learning Program