If a and ß are the zeroes of the polynomial : (1 Point) x² + 4x + 3, then the value of a2 B + ab2 will

Question

If a and ß are the zeroes of the
polynomial :
(1 Point)
x² + 4x
+ 3, then the value of a2 B + ab2 will

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Sarah 1 month 2021-08-13T01:04:37+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-13T01:06:23+00:00

    Correct Question –

    If  \alpha and \beta are zeros of polynomial x² + 4x + 3 , then find the value of  { \alpha }^{2}  \beta  +  { \beta }^{2}  \alpha

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    Answer

    Given –

    Quadratic Polynomial – x² + 4x + 3 whose zeros are  \alpha and  \beta

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    To find –

    { \alpha }^{2}  \beta  +  { \beta }^{2}  \alpha

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    Formula used –

    Sum of roots =  \alpha  +  \beta = -b/a

    Product of roots = \alpha \beta  = c/a

    where

    \longrightarrowa is coefficient of x²

    \longrightarrowb is coefficient of x

    \longrightarrowc is constant

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    Solution

    \longrightarrowa = 1

    \longrightarrowb = 4

    \longrightarrowc = 3

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    \longrightarrow[tex]\alpha + \beta = -4 [/tex]

    \longrightarrow[tex] \alpha \beta = 3 [/tex]

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    { \alpha }^{2}  \beta  +  { \beta }^{2}  \alpha  = \alpha  \beta ( \alpha  +  \beta )

    Substituting the value of  \alpha + \beta and  \alpha \beta

     { \alpha }^{2}  \beta  +  { \beta }^{2}  \alpha = 3 ( - 4 )

    = – 12

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    Thanks

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