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Relationship between Zeroes and Coefficients of a Polynomial

If α, β, γ ar...

Question

If $α, β, γ$ are the zeros of the polynomial $2 x^{3} + x^{2} - 13 x + 6$ then $α β γ = ?$

(a) -3 (b) 3 (c) $\frac{- 1}{2}$ (d) $\frac{- 13}{2}$

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Solution

$a x cubed plus b x squared plus c x plus d equals 0 i s space a space p o l y n o m i a l space a n d space alpha comma beta comma gamma space b e space t h e space z e r o s space o f space t h e space p o l y n o m i a l t h e n alpha cross times beta cross times gamma equals fraction numerator negative d over denominator space a end fraction i n space t h e s e space q u e s t i o n 2 x cubed plus x squared minus 13 x plus 6 equals 0 a equals 2 comma b equals 1 comma c equals negative 13 comma d equals 6 t h e n alpha cross times beta cross times gamma equals fraction numerator negative d over denominator space a end fraction alpha cross times beta cross times gamma equals fraction numerator negative 6 over denominator space 2 end fraction equals negative 3 o p t i o n space a space i s space c o r r e c t$

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