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

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

help me please

Answer 1

[Jos (10584)]

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 ...

[pitchaorn]

Thank you very much.

[Jos (10584)]

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

[pitchaorn]

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

[pitchaorn]

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.

Answer 2

[Image Analyst]

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]

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]

Thank you for answer

Answer 3

[Matt J]

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]

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]

Yes, i find soulution because your answer.Thank you for answer

Answer 4

[Sean de Wolski]

Obligatory one-liner:

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

[pitchaorn]

Thank you for answer