Which of the following is a solution of x2 − 2x = –8? negative 1 minus i square root of 28 1 plus i square root of 28 negative 1 minus i square root of 7 1 plus i square root of 7
Accepted Solution
A:
The correct answer choices are: ______________________________________________________ [C]: " 1 minus i square root of 7" ; { " x = 1 − i√7 " } ; AND: ______________________________________________________ [D]: " 1 plus i square root of 7" ; { " x = 1 + i√7 " } . ______________________________________________________ Explanation: ______________________________________________________ Given: ______________________________________________________
x² − 2x = - 8 ; ______________________________________________________ → Add "8" to EACH SIDE of the equation; to write this equation in "quadratic format" ; that is:
"a = 1 " {implied coefficient of "1"; since "any value; multiplied by "1", is equal to that same value"} ;
"b = -2" ;
"c = 8" ; ______________________________________________________ The quadratic equation formula is:__________________________________ x = [-b ± √(b²−4ac] / 2a ; = ? (Let us plug in our known values for "a, b, & c" x = { [-(-2] ± [√[(-2²) − (4*1*8)] } / {2* 1} ; x = [2 ± √(-2)] / 2 ;
x = [2 ± √(4 − 32)] / 2 ;
x = [2 ± √(-28)] / 2 ;
Note: Technically, "√-28" does not exist; since there is "no such thing as the square root of a negative number" . However, in mathematics, we have designated an "imaginary number", symbolized by the lower case letter, "i" ; to mean: " √-1 " ;