Question

If alpha and beta be the roots of the equation 2 - 3x - x^2 then find alpha and beta

Answer 1

Answer:

α = (-3 +√17)/2 , β = (- 3 - √17)/2

Step-by-step explanation:

x² +3x - 2 = 0

α and β are the roots of the equation 2 - 3x - x²

//sum of roots in quadratic equation ax²+ bx + c is -b/a and product of roots is c/a.

α + β = - (-3)/-1 = -3.

αβ = 2/-1 = -2

(α - β)² = (α + β)² - 4αβ = 9 + 8 = 17

α - β =  √17

Now solve for α and β

//add α+β and α - β

2α = -3+√17

α = (-3 +√17)/2

//Subtract α+β from α - β

2β = - 3 -√17

β = (- 3 - √17)/2