solve x²-3x-14 by factorisation method, completing square method and formula method
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 = ————————f
2A
In our case, A = -1
B = -3
C = -14
Accordingly, B2 - 4AC =
9 - 56 =
-47
Applying the quadratic formula :
3 ± √ -47
x = —————
-2
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,√ -47 =
√ 47 • (-1) =
√ 47 • √ -1 =
± √ 47 • i
√ 47 , rounded to 4 decimal digits, is 6.8557
So now we are looking at:
x = ( 3 ± 6.856 i ) / -2
Two imaginary solutions :
x =(3+√-47)/-2=3/-2-i/2√ 47 = -1.5000+3.4278i
or:
x =(3-√-47)/-2=3/-2+i/2√ 47 = -1.5000-3.4278i
Two solutions were found :
x =(3-√-47)/-2=3/-2+i/2√ 47 = -1.5000-3.4278i
x =(3+√-47)/-2=3/-2-i/2√ 47 = -
Step-by-step explanation:
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