# Thread: value of q in the equation

1. ## value of q in the equation

i tried to make this equation into q-2x^2 / x = 3x/x but cant make it to the next step... there seem no other value for q

how is it being shown ?

thanks

2. ## Re: value of q in the equation

need a little help in this equation guys...

3. ## Re: value of q in the equation

Your question is typed really awkwardly. I think it means

$\displaystyle \frac{q}{x} - 2x = 3$ has 4 as a root (for x).

If so, then x = 4...what are you struggling on?

4. ## Re: value of q in the equation

im struggling on how to get the 4 roots of the equation but q is there.... the only move i can make this is to q/x = 3 + 2x ; q = (2x + 3) x ; q = 2x^2 + 3x... im stuck here... to find the roots of the equation...

thanks

5. ## Re: value of q in the equation

Are there four roots for x? Or is 4 a root?

6. ## Re: value of q in the equation

because it is being indicated in the book i read... that is why ... how come it is 4... i wonder what number i have to manipulate here when there is x and q ... do i need to use discriminant here sir?

7. ## Re: value of q in the equation

as i understood 4 roots for x so , q must have value

8. ## Re: value of q in the equation

Clearly, there cannot be 4 roots. Multiplying both sides by x you obtain

$\displaystyle q - 2x^2 = 3x$

which is a second-degree polynomial, and only has two roots for x.

9. ## Re: value of q in the equation

With q = 44 (and I don't see why 44 is picked!), then solution is x = 4 or -5.5;
discriminant = 9 + 8q, so q => 9/8 for real solutions.
I guess I can see q = 44 IF problem stated: one of the 2 solutions is a positive integer (4 in this case).
(OR one of the solutions is a square...)

10. ## Re: value of q in the equation

Yes, if the problem stated that 4 is a root, clearly, q = 44.

11. ## Re: value of q in the equation

Originally Posted by rcs
as i understood 4 roots for x so , q must have value
That is, as you have been told, impossible. If you multiply both sides of $\displaystyle q/x- 2x= 3$ by x you get $\displaystyle q- 2x^2= 3x$ which is a quadratic equation and has, at most, 2 distinct roots. The original equation might have fewer solutions, but cannot have more so NO value of q gives the equation 4 roots.

If, on the other hand, you are saying that 4 is a root, we must have $\displaystyle q/4- 2(4)= 3$ so that $\displaystyle q/4= 11$ and then $\displaystyle q= 44$.

What is the exact statement of the problem in your text? You posted a picture in your first post, but that is something you wrote. Could you post a picture of the problem in the text?

12. ## Re: value of q in the equation

Originally Posted by HallsofIvy
That is, as you have been told, impossible. If you multiply both sides of $\displaystyle q/x- 2x= 3$ by x you get $\displaystyle q- 2x^2= 3x$ which is a quadratic equation and has, at most, 2 distinct roots. The original equation might have fewer solutions, but cannot have more so NO value of q gives the equation 4 roots.

If, on the other hand, you are saying that 4 is a root, we must have $\displaystyle q/4- 2(4)= 3$ so that $\displaystyle q/4= 11$ and then $\displaystyle q= 44$.

What is the exact statement of the problem in your text? You posted a picture in your first post, but that is something you wrote. Could you post a picture of the problem in the text?
This is it: What is the value of q so that (q/x) - 2x = 3 has 4 as a root?

13. ## Re: value of q in the equation

Originally Posted by rcs
This is it: What is the value of q so that (q/x) - 2x = 3 has 4 as a root?
If so, then we've already solved it like five times. Why does the original problem say that it has 4 roots?

14. ## Re: value of q in the equation

sorry sir... i must have overlooked it. but still i have to say thank you so much for the gift of intelligence you shared.

Millions of Thanks