Example 28. Find cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroe

1 thought on “Example 28. Find cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroe”

1. [tex]\huge\purple{\mid{\fbox{\underline{Answer:}}}\mid}\\\\[/tex]

   Given:–

   • sum of the product of its zeroes taken two at a time
   • the product of its zeroes as 5, -7, -14 respectively

   Find:–

   • Find cubic polynomial with the sum of the product of its zeroes.

   Answer:–

   Let the zeroes be α, β and γ.

   Then, we have

   α + β + γ = 5

   αβ + βγ + γα = -7

   αβγ = -14

   Now, required cubic polynomial

   => x³ – (α + β + γ)x² + (αβ + βγ + γα)x – αβγ

   => x³ – 5x² + (-7)x – (-14)

   => x³ – 5x – 7x + 14

   So, x³ – 5x – 7x + 14 is the required cubic polynomial which satisfy the given conditions.

   [tex]\\\\\\[/tex]

   HOPE IT HELPS

   PLEASE MARK ME BRAINLIEST ☺️

   Reply