How do you find the value of the discriminant and determine the nature of the roots #-4m^2-4m+5#?
In a quadratic function written in the form
the discriminant, also called delta is known as follow:
In the case of
Then using the formula for the discriminant...
When they ask about the 'nature of the roots' they what this basically means is, how many are there? You can know this from the descriminant.
(As for why they're called 'real' roots, you don't need to worry about that now)
So in this case, when
Given a quadratic of the form:
the discriminant is
For the given example:
So this expression has
The most common problem with this type of question is that we are typically accustomed to seeing this with
but the variable can be any letter (in this case it happens to be
#• " if "Delta>0" then 2 real irrational roots"#
#• " if "Delta>0" and a perfect square"#
#"then 2 real rational roots"#
#• " if "Delta=0" then real rational equal roots"#
#• " if "Delta<0" then 2 complex conjugate roots"#
#rArr"2 real and irrational roots"#
#color(blue)"As a check"#
#"solve for m using the "color(blue)"quadratic formula"#
#rArrm=-1/2+-1/2sqrt6larr" 2 real irrational roots"#
Two real solutions ,
If discriminant is positive, we get two real solutions, if it is zero we
get just one solution, and if it is negative we get complex solutions.
Here discriminant is positive, so we get two real solutions.