Hello all, wondering if you could give me a hand,
Prove that the equation 4=x(2-x) has no real roots.
Thanks in advance,
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.