How do you factorise x squared plus x plus 12?

Answer 1

x^2 + x + 12 = 0

You cannot factorize this equation in order to find real roots, but you can factorize it in order to find its complex roots as (x-r1)(x-r2)=0. Solve the equation by using the quadratic formula, find the complex roots, and then you are able to factorize it.

x ^2 +x + 12 = 0

x = (-1 + square root of (1 - 48))/2 or x = (-1 - square root of (1 - 48))/2

x = (-1 + square root of (- 47))/2 or x = (-1 - square root of (- 47))/2

By substituting -1 with i^2 we have:

x = (-1 + square root of (47i^2))/2 or x = (-1 - square root of (47i^2))/2

x = (-1 + i(square root of 47))/2 or x = (-1 - i(square root of 47))/2

x = -1/2 + i(square root of 47)/2 or x = -1/2 - i(square root of 47)/2

Now you are able to factorize the equation as: [x +(1/2 - ((square root of 47)/2)i))] [x +(1/2 +(square root of 47)/2)i))]

Well, let's make one addition to the comment you cannot factor this equation. When you factor an equation you are really factoring it over some field, such as real numbers, or rational numbers. ( look up fields if you are not familiar with them) This can be factored over the complex numbers, In fact, once you find two roots, call them, r1 and r2, you can always factor as (x-r1)(x-r2)=0. In this case the roots are complex, but the same would hold if they were real. Who wrote this comment is right, but I was talking about solving the equation by factoring, without using the quadratic formula. If we factorize the equation as (x - r1)(x - r2), we only presuppose that roots are complex roots, but we can find them only when we solve the equation by using the quadratic formula. So the meaning was that we can't solve this equation by factoring.

I appreciate the comment.