real roots

fred:

True or False Some cubic equations have no real roots and explain

Hi Fred,

All cubic equations have to have at least 1 real root. (unless you place restriction on the domain)

consider y=ax ³+bx ²+cx+d

As x approaches positive infinity the ax ³ term will have far more impact on the answer than any of the other terms. If a is positive, y will approach infinity.
As x approaches negative infinity the ax ³ term will have far more impact on the answer than any of the other terms. If a is positive, y will approach negative infinity.
(If a is negative it will be the other way around)

In order to get from y= -infinity to y= +infinity the curve must go through y=0 at least once. So there must be at least one real root.

do you understand what I am trying to say?

Here is a web page if you would like to take a look.

http://en.wikipedia.org/wiki/Cubic_function