Question

write the polynomial if the product and sum of the zeros are minus 1 upon 2 and 3 upon 2​

Answer 1

Answer:

Step-by-step explanation:

α+β= -1/2

α×β=3/2

x²-(α+β)x + α×β=0

x²-(-1/2)x+3/2=0

x²+x/2+3/2=0

2x²+x+3=0×2=0

So eqn is 2x²+x+3=0

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Answer 2

Hey,

$let \: \alpha \: and \: \beta \: be \: zeros \: of \: required \: polynomial \\ \\ given \: that \\ \alpha + \beta = \frac{3}{2} \: and \: \alpha \beta = \frac{- 1}{2} \\ \\ required \: polynomial \\ \\ x {}^{2} - ( \alpha + \beta )x + \alpha \beta \\ \\ = x {}^{2} - \frac{3x}{2} - \frac{1}{2} \\ \\ = 2x {}^{2} - 3x - 1$

I hope it helps you!!!