SOLUTION: Solve each equation. State the number and type of roots. 4. x^2+4=0

Algebra ->  Rational-functions -> SOLUTION: Solve each equation. State the number and type of roots. 4. x^2+4=0      Log On


   

Question 186580This question is from textbook alegbra2
: Solve each equation. State the number and type of roots.
4. x^2+4=0 This question is from textbook alegbra2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B4=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=0, and c=4


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%280%29+%2B-+sqrt%28+%280%29%5E2-4%281%29%284%29+%29%29%2F%282%281%29%29 Plug in a=1, b=0, and c=4


x+=+%28-0+%2B-+sqrt%28+0-4%281%29%284%29+%29%29%2F%282%281%29%29 Square 0 to get 0.


x+=+%28-0+%2B-+sqrt%28+0-16+%29%29%2F%282%281%29%29 Multiply 4%281%29%284%29 to get 16


x+=+%28-0+%2B-+sqrt%28+-16+%29%29%2F%282%281%29%29 Subtract 16 from 0 to get -16


x+=+%28-0+%2B-+sqrt%28+-16+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-0+%2B-+4%2Ai%29%2F%282%29 Take the square root of -16 to get 4%2Ai.


x+=+%28-0+%2B+4%2Ai%29%2F%282%29 or x+=+%28-0+-+4%2Ai%29%2F%282%29 Break up the expression.


x+=+%28-0%29%2F%282%29+%2B+%284%2Ai%29%2F%282%29 or x+=++%28-0%29%2F%282%29+-+%284%2Ai%29%2F%282%29 Break up the fraction for each case.


x+=+0%2B2%2Ai or x+=++0-2%2Ai Reduce.


x+=+2%2Ai or x+=+-2%2Ai Simplify.


So the answers are x+=+2%2Ai or x+=+-2%2Ai

Note: these solutions are complex (ie non real)