Question Number 1 :
For this equation x^2 + 81 = 0 , answer the following questions :
A. Find the roots using Quadratic Formula !
Answer Number 1 :
The equation x^2 + 81 = 0 is already in a*x^2+b*x+c=0 form.
By matching the constant position, we can derive that the value of a = 1, b = 0, c = 81.
1A. Find the roots using Quadratic Formula !
Use abc formula and you get either
x1 = (-b+sqrt(b^2-4*a*c))/(2*a) or x2 = (-b-sqrt(b^2-4*a*c))/(2*a)
As a = 1, b = 0 and c = 81,
we need to subtitute a,b,c in the abc formula, with thos values.
So we get x1 = (-(0) + sqrt( (0)^2 - 4 * (1)*(81)))/(2*1) and x2 = (-(0) - sqrt( (0)^2 - 4 * (1)*(81)))/(2*1)
Which make x1 = ( 0 + sqrt( 0-324))/(2) and x2 = ( 0 - sqrt( 0-324))/(2)
Which is the same with x1 = ( 0 + sqrt( -324))/(2) and x2 = ( 0 - sqrt( -324))/(2)
Which is the same as x1 = ( 0 + sqrt(324)*sqrt(-1))/(2) and x2 = ( 0 - sqrt(324)*sqrt(-1))/(2)
Because we know that sqrt(-1) = i,
We can get x1 = ( 18*i )/(2) and x2 = ( - 18*i )/(2)
We get following answers x1 = 0 + 9*i and x2 = 0 - 9*i
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