Equation

Equation
has one root x1 = 10. Determine the coefficient b and the second root x2.

Result

b =  1.6
x2 =  -8.4

Solution:

$$ \smash{ b=-(-1 \cdot 10 \cdot 10+84)/10 = \frac{ 8}{5 } = 1.6 \\~\\-x^2 +1.6x +84 =0 \\~\\x^2 -1.6x -84 =0 \\~\\D = 1.6^2 - 4\cdot 1 \cdot (-84) = 338.56 \\~\\D>0 \\~\\ \\~\\x_{1,2} = \frac{ 1.6 \pm \sqrt{ 1.6^2 - 4\cdot 1 \cdot (-84)} }{ 2 \cdot 1 } = \frac{ 1.6 \pm \sqrt{ 338.56 } }{ 2 } \\~\\x_{1,2} = 0.8 \pm 9.2 \\~\\x_{1} = 10 \\~\\x_{2} = -8.4 \\~\\ \\~\\ (x -10) (x +8.4) = 0 } $$








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