Question

if alpha and beta are the zeros of the polynomial 6x square - 7 x + 2 find a quadratic polynomial whose zeros are 1 by Alpha and one by beta​

Answer 1

Answer:2x square -7x+6

Step-by-step explanation:

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Answer 2

Required quadratic polynomial is

$x^2 -\dfrac{7}{2}x + 3$

Step-by-step explanation:

We are given the following quadratic equation in the question:

$6x^2-7x+2$

To find the roots of the equation:

$6x^2-7x+2 = \\6x^2-4x-3x+2 = 0\\2x(3x-2)-1(3x-2) = 0\\(2x-1)(3x-2) = 0\\\\x = \dfrac{1}{2}, \dfrac{2}{3}$

New roots:

$\alpha' = \dfrac{1}{\alpha} = 2\\\\\beta' = \dfrac{1}{\beta} = \dfrac{3}{2}$

Sum of new roots =

$\alpha' + \beta' = 2 + \dfrac{3}{2} = \dfrac{7}{2}$

Product of roots =

$\alpha' \times \beta' = 2\times \dfrac{3}{2} = 3$

New equation:

$x^2 - (\alpha' + \beta')x + (\alpha')(\beta')\\\\x^2 -\dfrac{7}{2}x + 3$

is the required quadratic equation.

#LearnMore

If alpha and beta are the zeros of the polynomial 2x2-5x+7 then find the quadratic polynomial whose zeores are 3alpha +4beta and 4alpha +3beta

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