1. ## completing the square

Hi everyone

1. Show that there is no real value of the constant c for which the equation

cx^2 + (4c+1)x + (c+2) = 0

2. Given that the roots of the equation x^2+ax+(a+2) = 0 differ by 2, find the possible values of the constant a. Hence state the possible values of the roots of the equation.

2. Originally Posted by emsypooh
2. Given that the roots of the equation x^2+ax+(a+2) = 0 differ by 2, find the possible values of the constant a. Hence state the possible values of the roots of the equation.
Hi

Let $\displaystyle x_1$ and $\displaystyle x_2$ the solutions of the equation x²+ax+(a+2) = 0

What relations can you write involving $\displaystyle x_1$ and $\displaystyle x_2$ ?

3. Originally Posted by running-gag
Hi

Let $\displaystyle x_1$ and $\displaystyle x_2$ the solutions of the equation x²+ax+(a+2) = 0

What relations can you write involving $\displaystyle x_1$ and $\displaystyle x_2$ ?
Hi there

I'm sorry, i sound so stupid, but i really don't know

4. The first one is of course $\displaystyle x_1 - x_2 = 2$ since you know that the roots differ by 2

Now you should also be able to write $\displaystyle x_1 + x_2 = ...$ and $\displaystyle x_1 \times x_2 = ...$

You should have learned this I suppose

5. nopeee, we havent learnt any of this. we went from factorizing to this.

so the answers are x1+x2 and x1 (times) x2?

6. Okay
Since $\displaystyle x_1$ and $\displaystyle x_2$ are the roots of x²+ax+(a+2) you can write
$\displaystyle x^2+ax+(a+2) = (x-x_1)(x-x_2)$

Expanding the RHS $\displaystyle x^2+ax+(a+2) = x^2-(x_1+x_2)x + x_1 x_2$

Therefore
$\displaystyle x_1 + x_2 =-a$
and
$\displaystyle x_1 x_2 = a+2$

Now you know $\displaystyle x_1 + x_2 =-a$ and $\displaystyle x_1 - x_2 =2$

That will give you $\displaystyle x_1$ and $\displaystyle x_2$ with respect to a

7. Originally Posted by running-gag
Okay
Since $\displaystyle x_1$ and $\displaystyle x_2$ are the roots of x²+ax+(a+2) you can write
$\displaystyle x^2+ax+(a+2) = (x-x_1)(x-x_2)$

Expanding the RHS $\displaystyle x^2+ax+(a+2) = x^2-(x_1+x_2)x + x_1 x_2$

Therefore
$\displaystyle x_1 + x_2 =-a$
and
$\displaystyle x_1 x_2 = a+2$

Now you know $\displaystyle x_1 + x_2 =-a$ and $\displaystyle x_1 - x_2 =2$

That will give you $\displaystyle x_1$ and $\displaystyle x_2$ with respect to a
thank you so, so, so, so much!!!! i really, really appreciate it

do you know how to work out the other question too? x

8. Originally Posted by emsypooh
thank you so, so, so, so much!!!! i really, really appreciate it

do you know how to work out the other question too? x
This one is not finished !

9. Originally Posted by running-gag
This one is not finished !

oh yeah whoops!

the full question is,

show that there is no real value of the constance c for which the equation

cx^2 + (4c+1)x + (c+2) = 0

has a repeated root.

whoops!

10. No

I mean the second exercise is not yet finished

11. aahhhh okay, i understand