Question

If alpha plus beta = 4 and alpha cube plus beta cube = 44 then alpha,beta are the zeros polynomial.

Answer 1

$3 {x}^{2} - 12x + 5$
is answer
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Answer 2

Answer:

According to the question if $\alpha +\beta =4$ and $\alpha^{3} + \beta^{3} = 44$ then alpha,beta are the zeros polynomial $3x^{2} -12x+5 = 0$.

Step-by-step explanation:

According to the question if $\alpha +\beta =4$ and $\alpha^{3} + \beta^{3} = 44$ then alpha,beta are the zeros polynomial.

$\alpha +\beta = 4\\\\\alpha ^{3} + \beta^{3} = 44\\\\or , (\alpha + \beta )^{3} - 3\alpha \beta (\alpha +\beta ) = 44\\\\ or , 64 - 12\alpha \beta = 44\\\\or, \alpha \beta = \frac{5}{3}$

The polynomial is

$x^{2} -(\alpha +\beta )x+\alpha \beta = 0\\\\or , x^{2} - 4x+ \frac{5}{3} = 0 \\\\ or , 3x^{2} -12x+5 = 0$

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