Question

Find a cubic polinomial with sum of roots ,sum of product of root taken 2 at a time of product of roots are 3,5 and -2

Answer 1

heya..!!!


given that:-

(alpha + beta + gamma) = 3

(alpha × beta + beta × gamma + gamma × alpha) = 5

AND,

(alpha × beta × gamma) = -2


we know that:-

the general formula for cubic Polynomial is:-

x³ - ( alpha + beta + gamma) x² + ( alpha×beta + beta + gamma × alpha ) x - alpha × beta × gamma


now, put the values in the Equation

we get,

x³ - (3)x² + (5)x - (-2)

=> x³ - 3x² + 5x + 2 = 0