maths

[15goddess15]

A4. Jenny had to solve x� - 4x = 0
She wrote: x� - 4x = 0
� x� = 4x
� x = 4
why was her answer not accepted ????

[R1Geezer]

presumably because it is not correct! if X squared = 4x then X = the square root of 4x

[R1Geezer]

sorry just got it there are 2 answers X = 4 or -4

[ladyalex]

x= +2 or -2

[ladyalex]

If you factorise x squared minus 4x, it gives
(x+2)(x-2), so x must equal either +2 or -2 to give
(x+2)(x-2)=0

[ladyalex]

OOPS I got it wrong.....
Are you sure that the initial equation is not
x squared -4 =0 ?
That would give x=+2 or x=-2

[ladyalex]

If the original equation is as you printed it, then Jenny's answer is correct.

X squared -4x =0
Therefore
x squared = 4x
divide both sides by x
x=4

Wish I hadn't started this now, I'm far to old to try to remember this.....

[heathfield]

X =4, but the equation can also be true where X= 0

[vascop]

You are all wrong - some more than others. This is a quadratic equation and so has 2 solutions. It can be written as
x(x-4)=0 and so x=0 or x-4=0. In other words
x=0 or 4.
So Jenny got one of the solutions but missed the other.
You can see that these are correct by substituting into the original equation:
0x0-4x0=0-0=0 and
4x4-4x4=0

[factor-fiction]

I agree with your answer vascop but you were wrong to say "You are all wrong ", because heathfield got it right.

[vascop]

I know, but he hadn't posted when I started my reply - we overlapped!

[derrynoose]

If both sides of an equation are divided by a factor which contains the "unknown", that factor must be written equal to zero. So where Jenny divided both sides by x, that x should have been written equal to zero, which gives the missing solution. That said, vascop's process is the best way to obtain all possible answers and applies equally to cubic equations; i.e. factorise, write each factor equal to zero and solve for x.