Find integral values of x for which x^4 - 3x^2 + 9 is a prime number

Question

Find integral values of x for which  x^4 - 3x^2 + 9  is a prime number

Bytelearn · Accepted Answer

Check Factoring: Let's first check if the expression can be factored. x^4 - 3x^2 + 9 This doesn't factor nicely with integer coefficients.Consider Integer Values: Now, let's consider the possible values of x that are integers. If x is an integer, x^4 and x^2 are also integers.Find Prime Expression: We need to find when x^4 - 3x^2 + 9 is prime. A prime number is only divisible by 1 and itself.Plug in Values: Let's plug in some values and check. For x = 0, we get 0^4 - 3(0)^2 + 9 = 9, which is not prime.Check x = 0: For x = 1, we get 1^4 - 3(1)^2 + 9 = 7, which is prime.Check x = 1: For x = -1, we get (-1)^4 - 3(-1)^2 + 9 = 7, which is also prime.Check x = -1: For x = 2, we get 2^4 - 3(2)^2 + 9 = 16 - 12 + 9 = 13, which is prime.Check x = 2: For x = -2, we get (-2)^4 - 3(-2)^2 + 9 = 16 - 12 + 9 = 13, which is also prime.Check x = -2: For x = 3, we get 3^4 - 3(3)^2 + 9 = 81 - 27 + 9 = 63, which is not prime.Check x = 3: For larger values of x, the expression will increase and not be prime. So, we don't need to check further.

Find integral values of $x$ for which $x^4 - 3x^2 + 9$ is a prime number

Full solution

More problems from Factor using a quadratic pattern

Related topics

Find integral values of xxx for which x4−3x2+9x^4 - 3x^2 + 9x4−3x2+9 is a prime number

Find integral values of $x$ for which $x^4 - 3x^2 + 9$ is a prime number