Question

Determine the number and type of complex solutions and possible real solutions for each of the following equations.

1) 2x^2 + 5x + 3 = 0

2) 4x^3 – 12x + 9 = 0

3) 2x^4 + x^2 – x + 6 = 0

Answer 1

@Michele_Laino

Answer 2

@mathmale

Answer 3

@robtobey

Answer 4

I have no idea where to even start

Answer 5

@Hero

Answer 6

"1) 2x^2 + 5x + 3 = 0 " is a quadratic equation in the form ax^2 + bx + c=0.
By comparing these two equations, determine the values of a, b and c.

a=
b=
c =

Now calculate the value of the "discriminant." This is defined as follows:\[discriminant=b^2-4ac\]

Answer 7

a =2
b=5
c=3

Answer 8

25-24=1

Answer 9

@mathmale

Answer 10

@mathmale

Answer 11

Sorry for the delay in my response. You did well in calculating the discriminant.

Here are the rules:

1. If the discriminant is positive, you have two real, different roots (e. g., x=4 and x=5)

2. If the discriminant is zero, you have two real, equal roots (e. g., x=2, x=2)

3. If the disc. is negative, you have two complex roots (e. g., x=2+i, x=2-i)

Which one of these cases do you have in this problem?

How would you describe the roots of your quadratic equation?

Answer 12

there are two real roots

Answer 13

now how would i find the roots? @mathmale

Answer 14

@Michele_Laino

Answer 15

for the first equation, it is suffice to apply the sandard formula:
\[\Large x = \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\]

Answer 16

Yes. Note, @18jonea, that you have already found b^2 - 4ac: it is 1.

So, subst. 5 for b in Michele's equation, above, and 2 for a.

then evaluate the two roots. Please share your work here.

Answer 17

\[x=\frac{ -b \pm \sqrt{1} }{ 2a }\]

Answer 18

\[x=-5\sqrt{1}\div4\]

Answer 19

Of course, simplify Sqrt(1) to just plain 1.

Answer 20

-5+1=-4/4=-1

Answer 21

Here, b=4 and a=2.

We must write the formula for x using parentheses:

x= [-5 plus or minus 1] / 4

Answer 22

-5-1=-6/4= -3/2

Answer 23

Try it, please. What is -5 plus 1? What is -5 minus 1? do this work BEFORE attempting to divide by 4.

Answer 24

Also, after writing one equation, move DOWN (not to the right) to type your next result.

Wrong: -5-1=-6/4= -3/2

Right: (-5-1)/4
= -6/4
= -3/2 (answer)

Answer 25

The roots are -1 and -3/2

Answer 26

is that correct?

Answer 27

yes! that's right!

Answer 28

Nice work, 18-J!

Answer 29

thank you, Michele!

Answer 30

:)

Answer 31

Ok Thank you so much could y'all help me with the other two as well please?

Answer 32

I know you have 2 more problems. Please start a new post for each, OK? Thanks.

Answer 33

Ok