Question

$\alpha = 2 \beta = 3 \gamma 4 = 4$
Find the cubic polynomial.
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Answer 1

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Answer 2

Answer:

α = 2, β = 3, $\gamma$ = 4

= (αβ + r) = 3

= (αβ + βr + αr) = -10

= αβr = -24

= k [$x^3$- (α + β + r) $x$² + (αβ + βr+ αr)]

= k [x3 – 2 + 3 + 4] $x$² + [(2) (3) + (3) (4) + (2) (4)]

= k ($x$³ – 9$x$² + 16 + 16)

= k = 1, p(x) = $x$³ – 9$x$² + 16$x$ + 16 = 0

=  $x$ - 4 ) $x$³ - 9$x$² + 16$x$ + 16 ( $x$² - 5$x$ - 4

             $x$³ - 4

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                  -5$x$² + 16

                  - 5$x^2$ + 20$x$

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                              -4 + 16

                              -4$x$ + 16

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                                    0

-----------------------------------------------------

=  $x$² - 5

= $x$³ – 9

= $x$² (

= ($x$ - 9) = 0

= $x$ = 9

= ($x$ + 16) = 0

= $x$ = 16