Question

Find a quadratic polynomial whose zeroes are the reciprocal of the zeros of 4x2-3x-1

Answer 1

there is steap by step explanation.

hope this will help you

Answer 2

New polynomial:

$x^2 +3x -4$

Step-by-step explanation:

We are given the following in the question:

$4x^2-3x-1$

To find the zeroes of the given polynomial:

$4x^2-3x-1 = \\4x^2 - 4x + x - 1 = 0\\4x(x-1)+1(x-1) = 0\\(4x+1)(x-1) = 0\\4x + 1 = 0, x - 1 = 0\\\\x = \dfrac{-1}{4}, x = 1\\\\\alpha = \dfrac{-1}{4}, \beta = 1$

New zeroes:

$\dfrac{1}{\alpha} = -4, \dfrac{1}{\beta} = 1\\\\\dfrac{1}{\alpha} + \dfrac{1}{\beta} = -3\\\\\dfrac{1}{\alpha}\times \dfrac{1}{\beta} = -4$

New polynomial:

$x^2 - (\dfrac{1}{\alpha} + \dfrac{1}{\beta}) + \dfrac{1}{\alpha}\times \dfrac{1}{\beta}\\\\x^2 +3x -4$

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