Question

if alpha and beta are the zeroes of the quadratic polynomial 6x^2 + x -2 then find the value of alpha - beta

Answer 1

Heya

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Alfa + Beta = -1/6

And

Alfa × Beta = -2/6 = -1/3

=>

Alfa - Beta = √{(Alfa + Beta)² - 4Alfa × Beta}

Alfa - Beta = √{ (1/36) + 4/3 }

=>

Alfa - Beta = √{147/108}

=>

Alfa - Beta = √{49/36}

=>

Alfa - Beta = 7/6

Answer 2

Answer:

α - β = 7/6

Step-by-step explanation:

Given Quadratic Equation is 6x² + x - 2.

a = 6, b = 1, c = -2.

(i) Sum of roots:

α + β = -b/a

α + β = -1/6

(ii) Product of roots:

αβ = c/a

αβ = -2/6

αβ = -1/3

Now,

∴ (α - β)² = (α + β)² - 4αβ

              = (-1/6)² - 4(-1/3)

              = 1/36 + 4/3

              = 49/36

∴ (α - β) = 7/6.

Hope it helps!