# How do you find the value of the discriminant and determine the nature of the roots #-4m^2-4m+5#?

##### 4 Answers

#### Explanation:

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...

So

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.

When

When

When

(As for why they're called 'real' roots, you don't need to worry about that now)

So in this case, when

Discriminant:

implying

#### Explanation:

Given a quadratic of the form:

the discriminant is

with

For the given example:

we have

So this expression has

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Note:

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

#### Explanation:

#Delta=b^2-4aclarrcolor(blue)" discriminant"#

#• " 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"#

#-4m^2-4m+5#

#"with "a=-4,b=-4,c=5#

#Delta=b^2-4ac=16+80=96#

#rArr"2 real and irrational roots"#

#color(blue)"As a check"#

#"solve for m using the "color(blue)"quadratic formula"#

#m=(4+-sqrt96)/(-8)=(4+-4sqrt6)/(-8)#

#rArrm=-1/2+-1/2sqrt6larr" 2 real irrational roots"#

**Two real solutions ,**

#### Explanation:

equation

Discriminant

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.