Don't Go on Multiplying

Algebra Level 1

Assume all the alphabets from $a$ to $z$ are assigned the values of their respective positions: $\begin{aligned} a &= 1 \\ b &= 2 \\ c &= 3 \\ &\vdots \\ z &= 26. \end{aligned}$ Find the value of $(x - a)(x - b)(x - c)(x - d)\cdots(x - z).$

The answer is 0.

2 solutions

Ram Mohith
Apr 30, 2018

If we observe the expression carefully we get :

$\color{#333333}(x - a)(x - b)(x - c)(x - d)(x - e)...........(x - w)\color{#D61F06}\boxed{(x - x)}\color{#333333}(x - y)(x - z)$

The expression in the red box will be $\color{#20A900}\text{ 0 because } x - x = 0$

$\therefore$ The final result will be $\color{#3D99F6}\boxed{0}$ .

You can use ( $\therefore$ ) instead of therefore.

Matin Naseri - 2 years, 10 months ago

You can, but all it accomplishes is obfuscating your explanation, especially when it's on an algebra problem for which many solvers will not be familiar with formal logical symbols.

Jordan Cahn - 2 years, 8 months ago

Oh my goodness xD Luckily I read this exact problem in a book ahaha

Winston Choo - 2 years, 8 months ago

Yes. There are many people who will post the exact problem everytime.

Ram Mohith - 2 years, 8 months ago

But I have posted it on April 30, 5 months back.

Ram Mohith - 2 years, 8 months ago

emmmmm....

ke xu - 1 year, 10 months ago

Rishabh Jain
Mar 12, 2019

Since in the sequence of multiplication there will come (x-x) which makes the whole product zero

Don't Go on Multiplying

The answer is 0.

2 solutions

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