What is the solution of 19x^2 + 13x + 54 = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The roots of a quadratic equation ax^2 + bx + c = 0 are: `(-b+-sqrt(b^2 - 4ac))/(2a)`

For the equation 19x^2 + 13x + 54 = 0, the roots are:

`(-13+-sqrt(13^2 - 4*19*54))/(38)`

= `(-13+-sqrt(169 - 4104))/(38)`

= `(-13+-sqrt(-3935))/(38)`

= `-13/38+i*sqrt(3935)/38` and `-13/38-i*sqrt(3935)/38`

The roots of the equation are `-13/38+i*sqrt(3935)/38` and `-13/38-i*sqrt(3935)/38`

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