Equation

Equation
2x2+bx+187=02x2+bx +187 =0
has one root x1 = 8. Determine the coefficient b and the second root x2.

Result

b =  -39.38
x2 =  11.69

Solution:

b=(2 8 8+187)/8=3158=39.38b=-(2 \cdot \ 8 \cdot \ 8+187)/8=- \dfrac{ 315 }{ 8 }=-39.38
2x239.375x+187=0  a=2;b=39.375;c=187 D=b24ac=39.375242187=54.390625 D>0  x1,2=b±D2a=39.38±54.394 x1,2=9.84375±1.84375 x1=11.6875 x2=8   Factored form of the equation:  2(x11.6875)(x8)=0 2x^2 -39.375x +187 =0 \ \\ \ \\ a=2; b=-39.375; c=187 \ \\ D = b^2 - 4ac = 39.375^2 - 4\cdot 2 \cdot 187 = 54.390625 \ \\ D>0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 39.38 \pm \sqrt{ 54.39 } }{ 4 } \ \\ x_{1,2} = 9.84375 \pm 1.84375 \ \\ x_{1} = 11.6875 \ \\ x_{2} = 8 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 2 (x -11.6875) (x -8) = 0 \ \\



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