Question

if alpha and beta are the zeros of the polynomial 6x square + x minus 2 find the value of one by Alpha Plus One by beta minus alpha beta

Answer 1

Hey

Here is your answer,

In attachment

Hope it helps you!

Answer 2

Answer:

$\frac{1}{\alpha}+\frac{1}{\beta}-\alpha \beta= \frac{5}{6}$

Step-by-step explanation:

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

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

a=6, b=1,c=-2,

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

$\implies \alpha+\beta=\frac{-1}{6}\:---(1)$

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

$\implies \alpha \beta=\frac{-2}{6}\\=\frac{-1}{3}\:---(2)$

$iii) \frac{1}{\alpha}+\frac{1}{\beta}\\=\frac{\alpha+\beta}{\alpha \beta}\\=\frac{\frac{-1}{6}}{\frac{-1}{3}}\\=\frac{1}{2}\:---(3)$

$\implies Now,\\\frac{1}{\alpha}+\frac{1}{\beta}-\alpha \beta\\=\frac{1}{2}-\frac{-1}{3}\\=\frac{1}{2}+\frac{1}{3}\\=\frac{3+2}{6}\\=\frac{5}{6}$

Therefore,

$\frac{1}{\alpha}+\frac{1}{\beta}-\alpha \beta= \frac{5}{6}$

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