Question

If alpha and beta are the zeros of the polynomial p(x)=3x²-4x-7 the form a quadratic polynomial whose zeros are 1/alpha and 1/beta

Answer 1

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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