InterviewSolution
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InterviewSolution
| 1. |
Derive quadratic formula |
| Answer» Start with\tax^2 + bx + c=0Divide the equation by a\tx^2 + bx/a + c/a = 0Put c/a on other side\tx^2 + bx/a = -c/aAdd (b/2a)2 to both sides\tx^2 + bx/a + (b/2a)^2 = -c/a + (b/2a)^2The left hand side is now in the x2 + 2dx + d2 format, where "d" is "b/2a"So we can re-write it this way:"Complete the Square" (x+b/2a)^2 = -c/a + (b/2a)^2Now x only appears once and we are making progress.Now Solve For "x"Now we just need to rearrange the equation to leave "x" on the left Start with (x+b/2a)^2 = -c/a + (b/2a)^2Square root\t(x+b/2a) = (+-) sqrt(-c/a+(b/2a)^2)Move b/2a to right\tx = -b/2a (+-) sqrt(-c/a+(b/2a)^2)That is actually solved! But let\'s simplify it a bit:Multiply right by 2a/2a\tx = [ -b (+-) sqrt(-(2a)^2 c/a + (2a)^2(b/2a)^2) ] / 2aSimplify:\tx = [ -b (+-) sqrt(-4ac + b^2) ] / 2a | |