Roots and coefficient

In the equation 2x2 + 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:

a=−3/2=−23​=−121​=−1.5  2⋅ a2+b⋅ a−9=0 2⋅ (−1.5)2+b⋅ (−1.5)−9=0  1.5b=−4.5  b=1.5−4.5​=−3  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​=2a−b±D​​=43±81​​ x1,2​=43±9​ x1,2​=0.75±2.25 x1​=3 x2​=−1.5  x2​=x1​=3

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