Roots and coefficient

In the equation 2x ^ 2 + bx-9 = 0 is one root x1 = -3/2. Determine the second root and the coefficient b.

Correct answer:

b =  -3
x₂ =  3

Step-by-step explanation:

$$\begin{gathered} a=-3\mathrm{/}2=-{\displaystyle \frac{3}{2}}=-1\frac{1}{2}=-1.5 \\ 2\cdot a^2+b\cdot a-9=0 \\ 2\cdot (-1.5{)}^2+b\cdot (-1.5)-9=0 \\ 1.5b=-4.5 \\ b=-3=-3 \end{gathered}$$

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