Question

if alpha and beta are the zeros of the polynomial 6 y square - 2 + Y, then the value of Alpha Beta + beta Alpha is ​

Answer 1

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${\large{\purple{\mathbb{ANSWER}}}}$

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Alpha and beta

Are zeroes of polynomial,

=》 6y²+y-2.

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Alpha beta + Beta alpha

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▪︎ In a quadratic equation product of zeroes

= Constant term/Coefficient of x²

${\large{\red{\boxed{\bold{=\:c/a}}}}}$

${\large{\blue{\bold{\underline{Therefore:-}}}}}$

=》 Alpha beta + beta alpha = Product of zeroes

= Alpha Beta + Alpha Beta

{Since a×b = b×a}

= (-2)/6 + (-2)/6

= -1/3 + -1/3.

= -1/3 - 1/3.

= -1-1/3.

${\large{\red{\boxed{\bold{=\:-2/3}}}}}$

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Answer 2

6y²+y-2=0

Comparing the given polynomial with ax²+ bx + c=0

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

Sum of zeroes=(α+β)=-b/a=-1/6

Product of zeroes = (αβ) = c/a=-2/6= -1/3

Now

$\alpha \beta + \beta \alpha = \frac{ - 1}{3} + \frac{ - 1}{3} = \frac{ - 2}{3}$