What is the improved quadratic formula to solve quadratic equations ?

Question

Savannah Anderson · Accepted Answer

There is only one quadratic formula, that is #x=(-b+-sqrt(b^2-4ac))/(2a)#.

For a general solution of #x# in #ax^2+bx+c=0#, we can derive the quadratic formula #x=(-b+-sqrt(b^2-4ac))/(2a)#. #ax^2+bx+c=0# #ax^2+bx=-c# #4a^2x^2+4abx=-4ac# #4a^2x^2+4abx+b^2=b^2-4ac# Now, you can factorize. #(2ax+b)^2=b^2-4ac# #2ax+b=+-sqrt(b^2-4ac)# #2ax=-b+-sqrt(b^2-4ac)# #:.x=(-b+-sqrt(b^2-4ac))/(2a)#

Genesis Allen · Answer

This could refer to...

A drawback of the quadratic formula is that it is frequently possible to simplify the square root by taking at least one extra step. This can be avoided if the middle coefficient is even by using a different formulation of the quadratic formula. Given: #ax^2+2dx+c = 0# The following formula yields the roots: #x = -d/a+-sqrt(d^2-ac)/a#

Julia Adams · Answer

undefined The improved quadratic formula is x = (-2c) / (b ± √(b² - 4ac)), which is derived from the standard quadratic formula ax² + bx + c = 0 by multiplying both sides by 4a, then completing the square.