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=32=1.5    2 a2+b a9=0 2 (1.5)2+b (1.5)9=0  1.5b=4.5  b=3
2x2+bx9=0  2 x2+(3) x9=0 2x23x9=0  a=2;b=3;c=9 D=b24ac=3242(9)=81 D>0  x1,2=b±D2a=3±814 x1,2=3±94 x1,2=0.75±2.25 x1=3 x2=1.5   Factored form of the equation:  2(x3)(x+1.5)=0  x2=x1=3

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