Question

If alpha,beta and gama are the zeros of the cubic polynomial x*3+5x-2 then find the values of (alpha + beta + gamma),[(alpha*beta)+(beta*gamma)+(gamma*alpha)] and (alpha*beta*gamma) also find the product of (alpha+beta+gamma),[(alpha*beta)+(beta*gamma)+(gamma*alpha)] and (alpha*beta*gamma)

Answer 1

Answer:

α + β + γ = 0.

αβ + βγ + γα = 5.

αβγ = 2.

Step-by-step explanation:

Given polynomial is  $x^{3} +5x-2$ .For which  α,β,γ are the zeroes.

Now,   α + β + γ = -(0)/(1) = 0.

           αβ + βγ + γα = (5)/1 = 5.

           αβγ = -(-2)/1 = 2.

Answer 2

Answer:

$\alpha + \beta + \gamma = \frac{ - b}{a} = 0$

$\alpha \beta + \beta \gamma + \alpha \gamma = \frac{c}{a} = - 5$

$\alpha \beta \gamma = \frac{ - d}{a} = 2$

& req. product = 0