How do you find the discriminant and how many solutions does $y= x^2 + 3x$ have?

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Answer 1 · 2015-05-08T19:56:08

The discriminant of an expression $ax^2+bx+c$ is
$Delta = b^2-4ac$
(extracted from the quadratic formula for solutions
$x= (-b+-sqrt(Delta))/(2a)$

Extend the quadratic in the given equation so it looks like the general form:
$y = (1)x^2 +3x +0$

$Delta = 3^2-4(1)(0) = 9$

If you look back to the quadratic formula you can see:

$Delta {(<0 rarr "no Real solutions"),(=0 rarr "exactly 1 solution"), (>0 rarr "2 solutions") :}$

In our case $Delta>0$
so $y=x^2+3x$ has 2 solutions

How do you find the discriminant and how many solutions does y= x^2 + 3xy= x^2 + 3x have?