3x^2 + 11x + 30
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Solve Quadratic Equation using the Quadratic Formula
3.3 Solving 3x2-11x+30 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 3
B = -11
C = 30
Accordingly, B2 - 4AC =
121 - 360 =
-239
Applying the quadratic formula :
11 ± √ -239
x = ——————
6
In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written (a+b*i)
Both i and -i are the square roots of minus 1
Accordingly,√ -239 =
√ 239 • (-1) =
√ 239 • √ -1 =
± √ 239 • i
√ 239 , rounded to 4 decimal digits, is 15.4596
So now we are looking at:
x = ( 11 ± 15.460 i ) / 6
Two imaginary solutions :
x =(11+√-239)/6=(11+i√ 239 )/6= 1.8333+2.5766i
or:
x =(11-√-239)/6=(11-i√ 239 )/6= 1.8333-2.5766i
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