# 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 result:

b =  -3
x2 =  3

#### Solution:

$a=-3/2=- \dfrac{ 3 }{ 2 }=-1.5 \ \\ \ \\ \ \\ \ \\ 2 \cdot \ a^2 + b \cdot \ a-9=0 \ \\ 2 \cdot \ (-1.5)^2 + b \cdot \ (-1.5)-9=0 \ \\ \ \\ 1.5b=-4.5 \ \\ \ \\ b=-3$

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