Question

if alpha and beta are zeros of the polynomial x square - 5 x + 6 then find the value of alpha + beta minus 3 alpha beta

Answer 1

the value of alpha+β-3alphaβ = -13

Answer 2

Answer:

$\alpha+\beta-3\alpha\beta\\=-13$

Step-by-step explanation:

$Given \: \alpha \: and \\\beta \: are \: zeroes \: of \: the\\polynomial \: x^{2}-5x+6$

$Compare \: given \: polynomial\\with \: ax^{2}+bx+c \: we \:get$

$a =1, b=-5,c=6$

$Sum\:of \: the\: zeroes \\=-\frac{-b}{a}$

$\implies \alpha+\beta=-\frac{-5}{1}=5$

$Product\:of\:the\: zeroes\\=\frac{c}{a}$

$\implies \alpha\beta=\frac{6}{1}$

$Now,\\\alpha+\beta-3\alpha\beta\\=5-3\times 6\\=5-18\\=-13$

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