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

Relationship Between Zeroes and Coefficients of a Cubic Polynomial

If α, β, γ ...

Question

If $α, β, γ$ be the zeroes of the polynomial $a x^{3} + b x^{2} + c x + d$ , then the value of $α β + β γ + γ α$ is-

\frac{- b}{a}

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

\frac{c}{a}

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

\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!

Open in App

Solution

The correct option is B $\frac{c}{a}$
If $α, β, γ$ are the zeroes of the cubic polynomial $a x^{3} + b x^{2} + c x + d$ , then the sum of the products of zeroes taken two at a time.
That is,
$αβ+βγ+γα=coeffiecient\ of xcoefficient\ of x3$
$\Rightarrow α β + β γ + γ α = \frac{c}{a}$
The correct answer is $B .$

Suggest Corrections

Similar questions

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

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

α β + β γ + γ α =

α, β, γ

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

= \frac{c}{a}

If $α, β$ and $γ$ are the zeros 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

Join BYJU'S Learning Program