1. Real Root 係咩? 2. Why the quadratic equation has to equal to zero?

1. Real Root -- root(s) of equation 要係 real no.(實數) -- 即不可含有 √ x ，where x -- +ve no.

e.g. of a real no. ：3/5, 0, -2.7, 4+√7, 2-3√5
e.g. of a non-real no.(imaginary no.虛數) : √ -2 ，√-4 , √-15 ，6-√-7

why √ -2 ，√-4 ， √-15 , ..... --- not a real no.？
∵ they do not exist in our " REAL" world！

e.g. √-4 = ？
2 x 2 = 4 ， -2 x -2 = 4 ， ∴ √-4 has no solution( no meaning) in our " REAL" world .
√-4 is just a symbol and √-4 does not exist in the real no. system (R)


2. Why the quadratic eqt. has to equal to zero?

(i) ax^2 + bx + c = 0 is the STANDARD FORM of a quadratic eqt.
From this standard form , we can easily find its root(s) by :
(a) factorization,
e.g. x^2 + x - 2 = 0
(x+2) (x-1) = 0
x = -2 or x = 1

(b) quadratic formula : x = 1/2a ( -b ± √b^2 - 4ac)
e.g. x^2 + x - 2 = 0
x = 1/2 ( -1 ± √1^2 - 4(1)(-2) = 1/2( -1 ± √9) =1/2 (2) or 1/2 (-4) = 1 or -2
(通常 quadratic formula 是 eqt. factorize 不到 才用 )

(ii) a quadratic equation 「可以 ≠ 0」，
∵它可以不是 in STANDARD FORM
e.g. x^2 + x - 2 = 0
<=> x^2 + x = 2
<=> x^2 = 2 - x
以上 3 條 都是 quadratic eqt，
而且 3 條都是 represent 同一的 quadratic eqt. -- roots ：-2 , 1