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⋅ a−9=0 2⋅ (−1.5)2+b⋅ (−1.5)−9=0  1.5b=−4.5  b=−3
2∗x2+b∗x−9=0  2⋅ x2+(−3)⋅ x−9=0 2x2−3x−9=0  a=2;b=−3;c=−9 D=b2−4ac=32−4⋅2⋅(−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(x−3)(x+1.5)=0  x2=x1=3

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