x^2 + 5x + 4 = 0
Describe the solution to the equation by just determining the discriminat.

Question

x^2 + 5x + 4 = 0 
Describe the solution to the equation by just determining the discriminat.

anonymous · Answer

@ganeshie8

ganeshie8 · Answer

find out the discriminant

anonymous · Answer

yup

anonymous · Answer

I have no clue how to tho

ganeshie8 · Answer

for a quadratic 
$\large ax^2+bx+c$,

$\large      b^2-4ac$ is called the discriminant

ganeshie8 · Answer

$\large   x^2 + 5x + 4 = 0 $

$\large  a =  ?$
$\large  b =  ?$
$\large  c =  ?$

anonymous · Answer

A= 0
B = 5
C = 4
?

ganeshie8 · Answer

good try, but A = 1 okay ?

anonymous · Answer

oh because x = 1 dur

ganeshie8 · Answer

$\large   x^2 + 5x + 4 = 0$

is same as 

$\large   1x^2 + 5x + 4 = 0$

ganeshie8 · Answer

so,

$\large a = 1$
$\large b = 5$
$\large c = 4$

ganeshie8 · Answer

find out the discriminant

anonymous · Answer

b2−4ac

anonymous · Answer

right

ganeshie8 · Answer

yes, evaluate

ganeshie8 · Answer

wat do u get ?

anonymous · Answer

hold on

anonymous · Answer

9

ganeshie8 · Answer

$\large a = 1$
$\large b = 5$
$\large c = 4$


discriminant = $\large  b^2 - 4ac = 5^2 - 4\times 1\times 4 = 25 - 16 = 9 $

ganeshie8 · Answer

Yes ! discriminant = $\large   9$

anonymous · Answer

dang
that was easy

ganeshie8 · Answer

yup :) but we're not done yet

ganeshie8 · Answer

we need to describe the type of solution by using this discriminant value

anonymous · Answer

oh

ganeshie8 · Answer

use below :

1) if discriminant > 0, then the equation will have "two different real solutions"
2) if discriminant = 0, then the equation will have "two same real solutions"
3) if discriminant < 0, then the equation will have "two complex solutions"

ganeshie8 · Answer

based on above conditions, wat do u think about the solutions for the given quadratic ?

anonymous · Answer

hmm do i plug in the 9 for x?

ganeshie8 · Answer

No, its much simpler than that

anonymous · Answer

ok please explain to me how because what you types up there made me totally lost

ganeshie8 · Answer

Since the discriminant = 9, which is greater than 0, the given equation will have "two different real solutions"

ganeshie8 · Answer

Moreover, since 9 is a perfect square, the solutions are rational as well.

anonymous · Answer

ok so that would be 9 < x < ?

ganeshie8 · Answer

Overall, the given equation will have "two different rational solutions"

ganeshie8 · Answer

we're done.

ganeshie8 · Answer

the question just asked u to describe the types of solutions

anonymous · Answer

?

anonymous · Answer

Ok that works thank you i still am wondering tho about that 9 and you said its a perfect square so

ganeshie8 · Answer

4, 9, 16, 25.... are perfect squares...

by any chance, do u remember the quadratic formula ?

anonymous · Answer

um is it like this$$b^2 +- √ $$

ganeshie8 · Answer

yes !

solutions =   $\large  \dfrac{-b \pm \sqrt{\text{discriminant}}}{2a}$

ganeshie8 · Answer

^^ discriminant goes and sits there

ganeshie8 · Answer

so, if discriminant is a perfect square, then there will not be any radicals in the solutions.

anonymous · Answer

OH

ganeshie8 · Answer

that means, the solutions will be rational numbers

ganeshie8 · Answer

for the present problem, just rephrase below :

Since the discriminant = 9, which is greater than 0, the given equation will have "two different real solutions"
Moreover, since 9 is a perfect square, the solutions are rational as well.
Overall, the given equation will have "two different rational solutions"

anonymous · Answer

So for the question i should say something like this: b2−4ac=52−4×1×4=25−16=9

anonymous · Answer

oh ok thank you the almighty GANESHINE

ganeshie8 · Answer

yes put that also :)