Question

If alpha beta gamma are distinct roots of the equation x^3-3x+11

Answer 1

Answer:

x² - 6x + 9

Step-by-step explanation:

If alpha beta gamma are the roots of the equation x2 - 3x + 11 then find the equation whose roots are (alpha + beta)

α & β are roots of x² - 3x + 11

=> α + β = - (-3)/1 = 3    (Sum of roots)

α + β  is roots of other equation

let say γ is roots of other equation

so  γ  =  α + β  = 3

Sum of roots = γ + γ = 3 + 3 = 6

Products of roots = γ * γ = 3 * 3 = 9

Equation

x² - 6x + 9

or Simply

(x - γ)(x - γ)

= (x-3)(x-3)

= (x -3)²

= x² - 6x + 9