Coefficient 21623

In the equation 2x2 + bx-9 = 0 there is one root x1 = -3 / 2. Determine the second root and the coefficient b

Correct answer:

b =  -3
x2 =  -3

Step-by-step explanation:

2x2 + bx​−9=0 x1​=−3/2=−23​=−121​=−1.5  2⋅ x1​⋅ x1​+b⋅ x1​−9=0 2⋅ (−1.5)⋅ (−1.5)+b⋅ (−1.5)−9=0  1.5b=−4.5  b=1.5−4.5​=−3  b=−3  b=(−3)=−3
2x2+3x−9=0  2x2+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​​=4−3±81​​ x1,2​=4−3±9​ x1,2​=−0.75±2.25 x1​=1.5 x2​=−3

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