Question

If alpha and beta are the zeroes of the polynomial 2x^2+3x+5 then fine the value of 1/alpha+1/beta

Answer 1

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${\huge{\purple{\mathbb{\bold{ANSWER}}}}}$

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

▪︎ Alpha and Beta are zeroes of polynomial:-

=》 2x² + 3x + 5.

▪︎ Let alpha be A and Beta be B for ease of writing.

${\large{\blue{\bold{\underline{To\:Find:-}}}}}$

▪︎ The value of 1/A + 1/B.

${\large{\blue{\bold{\underline{Concepts\:Used:-}}}}}$

▪︎ Sum of zeroes,

= coefficient of x/coefficient of x²

= -b/a.

▪︎ Product of zeroes,

= Constant term/Coefficient of x².

= c/a.

${\large{\blue{\bold{\underline{Now,}}}}}$

=》 1/A + 1/B

= A + B/AB.

{By Taking LCM}

= -(3)/2/5/2.

{Because sum of zeroes = -3/2 and product of zeroes = 5/2}

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

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