What is the quadratic formula?

2 Answers
Mar 26, 2018

Answer:

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

Explanation:

Negative b plus minus the square root of b squared minus 4*a*c over 2*a. To plug something into the quadratic formula the equation needs to be in standard form (#ax^2 + bx^2 +c #).

hope this helps!

Mar 27, 2018

Answer:

If we have:

# ax^2 + bx + c = 0 #

Then:

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

Explanation:

The quadratic formula provides a method of solving a generic quadratic equation:

# ax^2 + bx + c = 0 #

To solve the equation we first factor out #a#:

# a{x^2 + b/ax + c/a} = 0 => x^2 + b/ax + c/a = 0 #

Then we complete the square:

# (x + b/(2a))^2 - (b/(2a))^2 + c/a = 0 #

Now, we solve for #x#:

# (x + b/(2a))^2 = (b/(2a))^2 - c/a #
# " " = b^2/(4a^2) - c/a #

# " " = b^2/(4a^2) - (4ac)/(4a^2) #

# " " = (b^2-4ac)/(4a^2) #

By taking square root we get:

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

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

So that:

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

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

Which is known as the "quadratic formula".