Kindergarten equation
How many roots does it have :
x 3 − x 2 − 6 x + x 0 = 1
The answer is 2.
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2 solutions
R e w r i t t i n g e q u a t i o n x 3 − x 2 − 6 x = 0 F a c t o r i s i n g x ( x 2 − x − 6 ) = 0 = > x 2 − x − 6 = 0 ( x − 3 ) ( x + 2 ) = 0 t h e r e f o r e T h e 2 r o o t s a r e ; 3 , − 2 S o t h e a n s w e r i s 2
However the value of x = 0 will not be considered
As 0 0 IS UNDEFINED
You made a mistake .
When x × ( x 2 − x − 6 ) = 0 , It means that either x 2 − x − 6 = 0 or x = 0 .Or both cases might be possible.You did not include the case where x = 0 .
But if x = 0 then x 0 will be 0 0 which is undefined.
So we dont take 0 as one of the roots.
That's why we only take x 2 − x − 6 = 0 from which we get x = 3 , − 2
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Yea i dint consider x = 0 because it would be come undefined
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Well if you are writing a solution you should be including all cases right ?
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@Athiyaman Nallathambi – If it's undefined, meaning there's no solution at that value. . then why would it be included
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@Ralpho Madalpho – First take a look at the solution.If he had considered x = 0 and then explained why x 0 is undefined , then that's a good solution.Secondly when you have a × b = 0 , it means that either a = 0 or b = 0 or a = b = 0 . So its important to consider all 3 cases.
@Ralpho Madalpho – yes u r right but the whole equation cant get rejected only that x^0 will be get out from the equation.
what to so with x=0
Ok. Let's rewrite my equation in this form:
x 3 − x 2 − 6 x = 0 there x = 3, x = 0, x= -2
But if x = 0, 0 0 is undefined.
So, we have only two roots which satisfy my equation, 3 and -2