Question

Find a cubic polynomial whose zeroes are 2,3, and 4

Answer 1

zeros are

$\alpha + \beta + \gamma = - c \div a \\ \alpha \beta + \beta \gamma + \gamma \alpha = d \div a \\ \alpha \beta \gamma = - c \div a$

equation for finding cubic polynomial is x^3-(sum of zeros)+x^2+(sum of product of zeros)x-( product of zeros)

therefore, x^3-2x^2+3x-4 is the cubic polynomial

Answer 2

Answer:

x³-9x²+26x-24

Step-by-step explanation:

let α=2,β=3 and γ=4

standard form of cubic polynomial is [x³-(α+β+γ)x²+(αβ+βγ+γα)x-(αβγ)]  

therefore,

α+β+γ=2+3+4

         = 9

αβ+βγ+γα=2*3+3*4+4*2

                =26

αβγ=2*3*4

      = 24

now,putting the respective values in standard form of cubic polynomial

x³-(9)x²+(26)x-(24)

therefore required polynomial is: x³-9x²+26x-24