Convert Quadratic Functions From Standard Form To Intercept Form Or Vertex Form Worksheet By Nghi H Nguyen With Answers Page 2
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The unknown quantity d can be computed from the constants a, b, c by this relation (5):
d² = b² – 4ac (5)
We can easily obtain this relation by writing that the product (x1*x2) of the 2 real roots is equal
to (c/a).
(-b/2a + d/2a)(-b/2a – d/2a) = c/a
= 4ac d
b
– d
= b
– 4ac
²
²
²
²
If d ² = 0, there is double root at x = -b/2a
If d² > 0, there are 2 real roots.
If d² < 0, there are no real roots, there are complex roots.
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