Question

Which best explains why the expression plus or minus StartRoot b squared minus 4 a c EndRoot cannot be rewritten as b plus or minus StartRoot negative 4 a c EndRoot during the next step?

Answer 1

Explanation:

let the quadratic eq. be ax²+bx+c=0

or x²+b/a x+c/a=0

or x²+b/ax=-c/a

to complete the square add both sides (b/2a)²or b²/4a²

x²+b/a x+(b/2a)²=b²/4a² -c/a

(x+b/2a)²=(b²-4ac)/(4a²)

taking square root

`x+(b)/(2a) =\pm (√(b^2-4ac) )/(2a) \\or\\x=-(b)/(2a) \pm(√(b^2-4ac) )/(2a) \\or\\x=(-b \pm√(b^2-4ac) )/(2a)`

now you must know why -b and not +b