Verified answer

1/2x^2–x+5 = 0

This is a quadratic equation ( ax^2 + bx + c = 0)

a = 1/2 , b = -1 , c = 5

Solve this using the quadratic formula:

x = (-b +/- sqrt(b^2 - 4ac))/2a

x = (1 +/- sqrt ( 1 - 4(1/2)(5)))/2(1/2)

x = (1 +/- sqrt (1 - 10))/1

x = 1 +/- sqrt(-9)

x = 1 +/- sqrt(9.-1)

x = 1 +/- i sqrt(9) ( since i = sqrt(-1) )

So C.

There is another way , completing the square:

1/2x^2–x+5 = 0

1/2x^2 - x = -5

x^2 -2x = -10

x^2 -2x + 1 = -10 + 1 (The LHS becomes a perfect square)

(x - 1)^2 = -9

x - 1 = +/- sqrt(-9)

x = 1 +/- i sqrt(9)

question quantity a million : For this equation x^2 - x - 12 = 0 , answer here questions : A. discover the roots making use of Quadratic formula ! answer quantity a million : The equation x^2 - x - 12 = 0 is already in a*x^2+b*x+c=0 sort. via matching the consistent place, we can derive that the cost of a = a million, b = -a million, c = -12. 1A. discover the roots making use of Quadratic formula ! bear in mind the formula, x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a) We had understand that a = a million, b = -a million and c = -12, we merely ought to subtitute the cost of a,b and c in the abc formula. So x1 = (-(-a million) + sqrt( (-a million)^2 - 4 * (a million)*(-12)))/(2*a million) and x2 = (-(-a million) - sqrt( (-a million)^2 - 4 * (a million)*(-12)))/(2*a million) which could be became into x1 = ( a million + sqrt( a million+40 8))/(2) and x2 = ( a million - sqrt( a million+40 8))/(2) Which make x1 = ( a million + sqrt( 40 9))/(2) and x2 = ( a million - sqrt( 40 9))/(2) We have been given x1 = ( a million + 7 )/(2) and x2 = ( a million - 7 )/(2) So we've the solutions x1 = 4 and x2 = -3

½x² - x + 5 = 0

x² - 2x + 10 = 0

x = [2 ± √(2² - 4·1·10)]/(2·1)

 = [2 ± √(-36)]/2

 = [2 ± 6i]/2

 = 1 ± 3i, which is the same as 1 ± i√9

The answer is C. use this formula x=(-b+-sqrt(b^2-4ac))/2a.

-1 equals i^2.

With this information, you can solve this equation easily.

x = [-b+/-Sqrt(b^2 - 4ac]/2a

a = 1/2, b = -1 and c = 5

x = 1 ± i sqrt 9...C

1/2x^2 - x + 5=0

multiply each term by 2

2.1/2x^2-2.x+2.5=0

x^2-2x+10=0

a=1,b=-2,c=10

x=[-b+-sqrt(b2-4ac)]/2a

x=[2+-sqrt(4-4.1.10)]/2

x=1+-6i

none of above

C)