Question

ind the discriminant of the function f(x) = x2 - 4x + 5 and determine how many roots the function has.

Answer 1

u can take discriminant as \[b^2-4ac\]=\[(-4)^2-4*1*5=16-20=-4\]

Answer 2

the discriminant is

\[b^2 - 4ac\]

in your question a = 1, b = -4, c = 5

substitute

if

discriminant > 0 there are 2 unequal roots... and if the discriminant is a perfect square the roots are rational

discriminant = 0 there is 1 repeated root.

discriminant < 0 there are complex roots..... sometimes called undefined roots

Answer 3

A)
-36; 1 real root
B)
-36; 2 imaginary roots

C)
-4; 1 real root
D)
-4; 2 imaginary roots
not c

Answer 4

if the value is -4 there are 2 imaginary

Answer 5

I just would like to expand on campbell_st's post by explaining why this is so...

Recall that the quadratic formula states that:
\[(-b \pm \sqrt{b^2 - 4ac})/2a\]
The discriminant is the expression inside the root, namely \[b^2 - 4ac\]
If discriminant > 0, then we get:

\[(-b \pm \sqrt{discriminant} )/2a\] Which means the roots are:\[(-b + \sqrt{discriminant} )/2a\] and \[(-b - \sqrt{discriminant} )/2a\]

If discriminant = 0, then we get one root, which is:
\[(-b)/2a\]
//because the root of 0 is 0.

If the discriminant is < 0, then we get complex roots because the root of negative numbers yields complex numbers. \[\sqrt{-1} =i\]
^ i is a complex number