Question

.

Answer 1

Number of positive integers x for which f(x)= x^3 -8x^2 +20x -13 is a prime number

Answer 2

@ganeshie8

Answer 3

options ?

Answer 4

(A) 1
(B) 2
(C) 3
(D) 4

Answer 5

may be start by factoring the cubic using rational root theorem

Answer 6

Hint :-
consider x=2n or x=2n+1

for x>4

when x is odd then its devide 2
when x is even then its devide 5

only 2 primes when x=2,4

Answer 7

can we agree that \(N = ab\) is a prime => a = 1 or b = 1

Answer 8

ikram, x=2,3,4

3 primes right ?

Answer 9

f(x)= x^3 -8x^2 +20x -13 is composite for all x>4
prove :-
for x odd x=2n+1
bla bla bla xD

for x=2n we can't conclude and since its even we consider
x=2 ( 5n+r)

xD need to check 5 cases

Answer 10

yes yes three primes sorry ^^

Answer 11

nice :)

Answer 12

why they give this for kids ?
idk how to solve it in other way lol

Answer 13

ok so factorize

Answer 14

other way is to use the simple fact \(N=ab\) => a=1 or b = 1

Answer 15

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

yes

f(1) = 1 - 8 + 20 - 13 = -12 + 12 = 0

=> (x-1) is a factor of f(x)


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

Answer 16

x-1 =1 yields
x=2 and x^2-7x+13 = 3

x^2-7x+13 = 1 yields
x = 3, 4 and x-1 = 2, 3

Answer 17

so x = 2, 3, 4 are the only possible integers

Answer 18

sweet >.>
i can't let NT get out of my head lol

Answer 19

division algorithm is a straightforward method !

Answer 20

Sorry , for late reply , i have problem with internet

Answer 21

DA is general and can be tried for ANY polynomial i guess
but this N=ab method is just a special case...

Answer 22

haha yep :3