Can this formula be used for any quadratic equation?

epoddoulc

See the pic below

(edited 7 years ago)

Yeah, but sometimes it is easier to factorise or complete the square.

(edited 7 years ago)

Reply 3

PythagorasGhost

Yes, it's what you get when you complete the square on the equation ax^2 + bx + c = 0.
Hence, you substitute your values for a, b and c (e.g. a=3, b=2 and c=-1 for 3x^2 + 2x - 1 = 0) to find the solutions of the equation.

Note that b^2 - 4ac >= 0 for there to be ('real') solutions (since you can't square root a negative number).

(edited 7 years ago)

Reply 4

Kallisto

Entertainment Forum Helper

Yeah, you can. If you solve the general quadratic formula step by step, you get what you have written above. See here.

Start with multiplying by 4a as first step, completing the square with b² on each side of the equation then. The rest is just solving to value x.