Question

Find a cubic polynomial
with the sum of the product of its Zeroes of two at a time, and product of its Zeroes as 4, 1 and -6 respectively​

Answer 1

$\alpha + \beta + \gamma = 4$

$\alpha \beta + \beta \gamma + \alpha \gamma = 1 \\ \alpha \beta \gamma = - 6$

$p{x} = {x}^{3} - ( \alpha + \beta + \gamma ) {x}^{2} + ( \alpha \beta + \beta \gamma + \alpha \gamma )x - \alpha \beta \gamma$

$p{x} = {x}^{3} - 4 {x}^{2} + x + 6$

Answer 2

Answer:

x³-4x²+x+6=0

Step-by-step explanation:

Sum of its zeros=4

sum of the product of its Zeroes of two at a time=1

product of its Zeroes=(-6)

Skeletal Cubic Equation:-

x³-(sum of roots)x²+(sum of the product of its Zeroes of two at a time)x-(product of its Zeroes)=0

x³-(4)x²+(1)x-(-6)=0

x³-4x²+x+6=0

Hence,the Required Cubic Polynomial is x³-4x²+x+6.