Question

if alpha and beta are zeroes of the polynomial p(x) =3x² -2x -6 then find 1/ alpha + 1/ beta
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Answer 1

Answer:

p(x) = 3x²-4x-7

      = 3x²+3x-7x-7

      = 3x(x+1) -7(x+1)

      = (3x-7)(x+1)

3x - 7 = 0 ------> x = 7/3

x+1 = 0     -------> x = -1

Therefore,

α = 7/3

β = -1

Therefore,

1/α = 3/7

1/β = -1

Hence the quadratic polynomial having zeroes 1/α and 1/β is

(x - 1/α)( x - 1/β) = x² - x(1/α + 1/β) + 1/αβ

                         = x² - x(3/7 - 1) -3/7

                         = x² - x(-4/7) - 3/7

                         = 7x² + 4x - 3    (Multiplying all the terms by 7)

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Step-by-step explanation: