Question

Find a cubic polynomial whose zeroes are -5 ,4,6

Answer 1

Let α, β and γ be three zeroes of the cubic polynomial.

Given:

α = - 5, β = 4 and γ = 6

We have to find, the value of cubic polynomial whose zeroes are - 5 , 4 and 6.

Solution:

We know that,

The cubic polynomial whose zeroes are α, β and γ.

$x^{3}$ - (α + β + γ)$x^2$ + (αβ + βγ + γα)x - αβγ

= $x^{3}$ - (- 5 + 4 + 6)$x^2$ + [(- 5)(4) + 4(6) + 6(- 5)]x - (-5)(4)(6)

= $x^{3}$ - (5)$x^2$ + (- 20 + 24 -30)x + 120

= $x^{3}$ - 5$x^2$ - 26x + 120

Thus,  the value of cubic polynomial whose zeroes are - 5 , 4 and 6 is "$x^{3}$ - 5$x^2$ - 26x + 120".