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

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

3. Originally Posted by running-gag
Hi

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

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

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

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

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

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 $x_1$ and $x_2$ are the roots of x²+ax+(a+2) you can write
$x^2+ax+(a+2) = (x-x_1)(x-x_2)$

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

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

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

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

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

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

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

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

That will give you $x_1$ and $x_2$ 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