# Thread: Can you... Prove that

1. ## Can you... Prove that

Hello all, wondering if you could give me a hand,

Prove that the equation 4=x(2-x) has no real roots.

Max

2. Expand, move everything to one side, so that you have a quadratic of the form $\displaystyle ax^2 + bx + c = 0$.

Then check the discriminant. If the discriminant is negative, then there are not any real roots.

3. Thanks a lot, I get it now.

Max

4. Originally Posted by Max888
Hello all, wondering if you could give me a hand,

Prove that the equation 4=x(2-x) has no real roots.

Max
Alternatively, here's how Fred Flinstone might have done it...

$\displaystyle 4=x(2-x)$

$\displaystyle x(x-2)=-4$

$\displaystyle (a\ number)(a\ value\ 2\ less\ than\ that\ number)=-4$

$\displaystyle 1(-1)=-1$

To get a $\displaystyle -4,$ we need a $\displaystyle +4$ instead of 1

or a $\displaystyle -4$ instead of $\displaystyle -1$

Apart from those, we need $\displaystyle (2)(-2)$ or $\displaystyle (-3.?)(1.?)$

or $\displaystyle (-1.?)(3.?)$

or $\displaystyle (4.?)(-0.?)$ etc, etc none of which can differ by 2

Much quicker to know the "abc" formula.

5. Right, thanks a lot!