find it

Number Theory Level 2

find the number of integer values of x for which the function is a prime number

f(x) = $x^{3} - 8x^{2} + 20x -13$

Please post your solution too

1 solution

U Z
Oct 10, 2014

we can see that 1 is the root of the equation

therefore when dividing the polynomial with (x -1)

we get

$(x-1)(x^{2} - 7x +13)$ = f(x)

thus for f(x) to be a prime number we should have

$(x-1)(x^{2} - 7x +13)$ = 1

thus

(x -1 )= 1 or (x -3)(x - 4) = 1

therefore 3 solutions

Is $x$ any real number? If so, there are infinitely many values in which is it is a prime number.

Can you clarify what you mean in the last part?

Calvin Lin Staff - 6 years, 8 months ago

Thank you sir edited

Sir I want to post a question of which I have a very good graphical solution so sir how can I attach an image to my solution

Edit: avatar avatar

U Z - 6 years, 8 months ago

you can use markdown to display an image. Use:

  ![title](url link)

I've edited your comment to give you an example.

Calvin Lin Staff - 6 years, 8 months ago