3x square+6x-25:factions
Answers
Answer:
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 = 6
C = -25
Accordingly, B2 - 4AC =
36 - 300 =
-264
Applying the quadratic formula :
-6 ± √ -264
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,√ -264 =
√ 264 • (-1) =
√ 264 • √ -1 =
± √ 264 • i
Can √ 264 be simplified ?
Yes! The prime factorization of 264 is
2•2•2•3•11
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 264 = √ 2•2•2•3•11 =
± 2 • √ 66
√ 66 , rounded to 4 decimal digits, is 8.1240
So now we are looking at:
x = ( -6 ± 2 • 8.124 i ) / -6