CameraIcon

SearchIcon

MyQuestionIcon

1

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

Zeroes of a Quadratic Polynomial

Find a cubic ...

Question

Find a cubic polynomial whose zeros are $α, β$ and $γ$ such that $(α + β + γ) = 4, (α β + β γ + γ α) = 1$ and $α β γ = - 6$ .

Open in App

Solution

A cubic polynomial whose zeros are $α, β$ and $γ$ is given by
$p (x) = x^{3} - (α + β + γ) x^{2} + (α β + β γ + γ α) x - α β γ$
Thus, the cubic polynomial is
$p (x) = x^{3} - (4) x^{2} + (1) x - (- 6)$
$p (x) = x^{3} - 4 x^{2} + x + 6$

Suggest Corrections

thumbs-up

3

Similar questions

α, β

γ

are the zeros of the cubic, polynomial

3 x^{3} - 5 x^{2} - 11 x - 3

α + β + γ

α, β

γ

are the zeroes of the polynomial

{2 x}^{3} + x^{2} - 13 x + 6

α β γ

α, β

γ

are the roots of the equation

x^{3} - x - 1 = 0

then the value of,

\frac{1 + α}{1 - α} + \frac{1 + β}{1 - β} + \frac{1 + γ}{1 - γ}

α, β

γ

be distinct real numbers. The points whose position vectors are

α^i + β^j + γ^k

β^i + γ^j + α^k

γ^i + α^j + β^k

α, β, γ

are modulus of the complex number

3 + 4 i, - 5 + 12 i, 1 - i

, then the increasing order for

α, β

γ

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Zeros of a Quadratic Polynomial

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Zeroes of a Quadratic Polynomial

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon