Question

if alpha and beta are zeros of the polynomial 2 X square + 7 x + 3 then find the value of Alpha square plus beta square minus 2 alpha beta

Answer 1

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Answer 2

Answer:

$Value \: of \\\alpha^{2}+\beta^{2}-2\alpha\beta=\frac{49}{4}$

Step-by-step explanation:

$Given\:\alpha \:and\:\beta\\are\: zeroes\:of\:the\:\\polynomial \:2x^{2}+7x+3$

Compare given Quadratic expression by ax²+bx+c , we get

a = 2 , b = 7, c = 3

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

$\implies \alpha+\beta=\frac{-7}{2}\:---(1)$

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

$\implies \alpha \beta=\frac{3}{2}\:---(2)$

$Now,\\\alpha^{2}+\beta^{2}-2\alpha\beta\\=(\alpha+\beta)^{2}\\=\left(\frac{-7}{2}\right)^{2}\\=\frac{49}{4}$

Therefore,

$\alpha^{2}+\beta^{2}-2\alpha\beta=\frac{49}{4}$

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