## How to do that.the product of four consecutive even integers is 13440. Using Matlab?

on 20 Sep 2013

### Jos (10584) (view profile)

the product of four consecutive even integers is 13440. Using Matlab's build-in function for operations with polynomials, determine the four integers.

I don't know how to do that

answer is 8 10 12 14

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### Jos (10584) (view profile)

on 20 Sep 2013

One approach is to use brute force:

```N = 13440 ;
for k = 2:N
v = k + [0:2:6] ;
p = prod(v) ;
if prod(v)==N,
disp('N is the product of :') ;
disp (v)
break
elseif prod(v) > N
disp('There is no solution')
break
end
end
```

There are many optimalisations that can be made ...

Jos (10584)

### Jos (10584) (view profile)

on 20 Sep 2013

Note that this does not use polynomials, so it is not a real answer to your (homework?) question ...

pitchaorn

### pitchaorn (view profile)

on 20 Sep 2013

Yes, I think my teacher want my answer make from polynomials.

pitchaorn

### pitchaorn (view profile)

on 23 Sep 2013

Your answer is correct so thank you. But I change v to v=x*(x+2)*(x+4)*(x+6) and if v==N. My teacher told me "x*(x+2)*(x+4)*(x+6)" is polynomials.

### Image Analyst (view profile)

on 20 Sep 2013

y = x*(x+2)*(x+4)*(x+6)

= x*(x+2)*(x^2+10X+24)

= x * ( x^3+10x^2+24x + 2x^2+20X+48)

= x^4 + .... and so on.

Then subtract 13440 and use fzero to determine the root. Perhaps that's what he meant.

Image Analyst

### Image Analyst (view profile)

on 20 Sep 2013

Visualizing it helps:

```x = -20:10;
y = x.*(x+2).*(x+4).*(x+6);
plot(x,y, 'bs-', 'LineWidth', 3);
xl = xlim;
% Plot a horizontal line at y = 13440
line([xl(1), xl(2)], [13440, 13440], ...
'Color', [1,0,0], 'LineWidth', 3);
grid on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
```
pitchaorn

on 23 Sep 2013

on 20 Sep 2013
Edited by Matt J

### Matt J (view profile)

on 20 Sep 2013

Hint: What if you solved the polynomial equation

` x*(x+2)*(x+4)*(x+6)=13440`

using MATLAB's commands POLY and ROOTS?

Matt J

### Matt J (view profile)

on 20 Sep 2013

If you follow this approach, you will also find that an additional solution is [-14 -12 -10 -8], which might earn you bonus points!

pitchaorn

on 23 Sep 2013

### Sean de Wolski (view profile)

on 20 Sep 2013

Obligatory one-liner:

```vals = 2*find(prod(bsxfun(@plus,(2:2:13440).',0:2:6),2)==13440)+[0:2:6]
```

pitchaorn

on 23 Sep 2013