What is the quadratic formula?
2 Answers
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 (
hope this helps!
If we have:
ax^2 + bx + c = 0 ax2+bx+c=0
Then:
x = (- b +-sqrt(b^2-4ac))/(2a) x=−b±√b2−4ac2a
Explanation:
The quadratic formula provides a method of solving a generic quadratic equation:
ax^2 + bx + c = 0 ax2+bx+c=0
To solve the equation we first factor out
a{x^2 + b/ax + c/a} = 0 => x^2 + b/ax + c/a = 0 a{x2+bax+ca}=0⇒x2+bax+ca=0
Then we complete the square:
(x + b/(2a))^2 - (b/(2a))^2 + c/a = 0 (x+b2a)2−(b2a)2+ca=0
Now, we solve for
(x + b/(2a))^2 = (b/(2a))^2 - c/a (x+b2a)2=(b2a)2−ca
" " = b^2/(4a^2) - c/a =b24a2−ca
" " = b^2/(4a^2) - (4ac)/(4a^2) =b24a2−4ac4a2
" " = (b^2-4ac)/(4a^2) =b2−4ac4a2
By taking square root we get:
x + b/(2a) = +-sqrt((b^2-4ac)/(4a^2)) x+b2a=±√b2−4ac4a2
" " = +-sqrt(b^2-4ac)/(2a) =±√b2−4ac2a
So that:
x = - b/(2a) +-sqrt(b^2-4ac)/(2a) x=−b2a±√b2−4ac2a
:. x = (- b +-sqrt(b^2-4ac))/(2a)
Which is known as the "quadratic formula".
