# We have to solve the following equation (the matix in the document). How am i meant to figure out what a=? i have done some working but i am not sure what ot do next. i am not sure what to do...

We have to solve the following equation (the matix in the document).

How am i meant to figure out what a=?

i have done some working but i am not sure what ot do next.

i am not sure what to do with the 9. I have factorised the forst part.

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embizze | Certified Educator

You have correctly found the determinant to be `x^3-5x^2+3x+9`

Since the matrix is singular the determinant is zero so:

`x^3-5x^2+3x+9=0`

There are a number of ways to try to factor this. The only possible rational roots are `+-1,+-3` so it doesn't hurt to try them. You will find that 3 is a root so (x-3) is a factor.

`(x-3)(x-3)(x+1)=0`

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The two solutions are x=3 (double root) and x=-1

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You can also use graphing technology to check for the roots. Real roots will be the x-intercepts of the graph of `y=x^3-5x^2+3x+9` .

lilian-0716 | Student

how do we know that the only possible rational roots are +-1 and +-3?

lilian-0716 | Student

Hi

can you please explain how you got

and why do we take 1 and 3 as possible roots?