If α, β, γ are the roots of cubic equation a $x^{3}$ + cx = 0. Find the value of $α^{3}$ + $β^{3}$ + $γ^{3}$ .

__

Open in App

Solution

Solution: For a $x^{3}$ + cx = 0

= x(a $x^{2}$ + c) = 0

x = 0 or a $x^{2}$ + c = 0

From the above equation we conclude that one root of equation a $x^{3}$ + cx should be zero

and Sum of the root = α + β + γ = 0

We know $α^{3}$ + $β^{3}$ + $γ^{3}$ = 3αβγ

Since one root is zero

3αβγ = 0

So, $α^{3}$ + $β^{3}$ + $γ^{3}$ = 0

Suggest Corrections

Similar questions

Q. If

α, β, γ

are the roots of the equation

x^{3} + 4 x + 2 = 0

, then

α^{3} + β^{3} + γ^{3} =

Q. If

α, β, γ

are the roots of the cubic

x^{3} - 2 x + 3 = 0

, then value of

\frac{1}{α^{3} + β^{3} + 6} + \frac{1}{β^{3} + γ^{3} + 6} + \frac{1}{γ^{3} + α^{3} + 6}

is equal to

Q. If

α, β, γ

are the roots of a cubic equation satisfying the relations

α + β + γ = 2

α^{2} + β^{2} + γ^{2} = 6

and

α^{3} + β^{3} + γ^{3} = 8

, then the equation is:

Q. If

α, β, γ

are the roots of

x^{3} + l x + m = 0

, then the value of

α^{3} + β^{3} + γ^{3}

If α, β, γ are the roots of $x^{3}$ + 3x + 2 = 0. Find the equation whose roots are $α^{3}$ , $β^{3}$ , $γ^{3}$ . Also find the value of $α^{3}$ + $β^{3}$ + $γ^{3}$ - 3αβγ.

Join BYJU'S Learning Program

If α, β, γ are the roots of cubic equation a x3 + cx = 0. Find the value of α3 + β3 + γ3. __

Solution: For ax3 + cx = 0 = x(ax2 + c) = 0 x = 0 or ax2 + c = 0 From the above equation we conclude that one root of equation ax3 + cx should be zero and Sum of the root = α + β + γ = 0 We know α3 + β3 + γ3 = 3αβγ Since one root is zero 3αβγ = 0 So,α3 + β3 + γ3 = 0

If α, β, γ are the roots of cubic equation a $x^{3}$ + cx = 0. Find the value of $α^{3}$ + $β^{3}$ + $γ^{3}$ .

__