# Thread: Find the real-number solutions of the equation

1. ## Find the real-number solutions of the equation

x^3 +7x^2 +4x +28 = 0

I don't know how to type these problems out on the computer, so I hope you understand. Here's where I started and then got lost.

x(x^2 + 7x + 4....... that s as far as I got. Please help it makes no sense to me!

2. ## Re: Find the real-number solutions of the equation

Originally Posted by dtbrunson

x^3 +7x^2 +4x +28 = 0

I don't know how to type these problems out on the computer, so I hope you understand. Here's where I started and then got lost.

x(x^2 + 7x + 4....... that s as far as I got. Please help it makes no sense to me!
Hi dtbrunson,

You didn't notice you could factor this expression by grouping, did you?
Well, you can.

$x^3+7x^2+4x+28=0$

Group the first two terms and factor out $x^2}$
Then, group the last two terms and factor out a 4.

$x^2(x+7)+4(x+7)=0$

Now you have: $(x^2+4)(x+7)=0$

Looks like 1 real and 2 imaginary solutions.

3. ## Re: Find the real-number solutions of the equation

Thanks but what do you mean when you say 1 real and 2 imaginary? Does it go further than that?
(x^2 + 4) (x + 7)
x(x+4) (x+7)?.......

4. ## Re: Find the real-number solutions of the equation

Thanks but what do you mean when you say 1 real and 2 imaginary? Does it go further than that?
(x^2 + 4) (x + 7)
x(x+4) (x+7)?.......

5. ## Re: Find the real-number solutions of the equation

Originally Posted by dtbrunson
Thanks but what do you mean when you say 1 real and 2 imaginary? Does it go further than that?
(x^2 + 4) (x + 7)
x(x+4) (x+7)?.......
That's factored incorrectly. Start here:

$(x^2+4)(x+7)=0$

Use the 'zero product property' to set each factor to zero and solve.

$x^2+4=0$

$x^2=-4$

$x=\pm 2i$

These are your two imaginary zeros.

$x+7=0$

$x=-7$

This is your one real zero.

6. ## Re: Find the real-number solutions of the equation

Originally Posted by dtbrunson
(x^2 + 4)
x(x+4)
NO. x(x + 4) = x^2 + 4x, NOT x^2 + 4.

And if you don't understand what masters just told you, then you need help ftom your teacher...

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