Solve by factoring.
n^2+n-12=0
I know i would need to factor it and then use the zero product property, but there is a variable instead of a variable attached with a constant.
for example,
k^2+7k+12=0
so it must be (k+3)(k+4) because k*k=k^2, 4+3=7 and 4*3=12.
But there is no constant by the "n" except for 1 but it doesnt make sense...
Anyone?
To solve the quadratic equation n^2 + n - 12 = 0 by factoring, you need to find two numbers whose product is equal to the product of the coefficient of the quadratic term (in this case 1) and the constant term (in this case -12), and whose sum is equal to the coefficient of the linear term (in this case 1).
In this case, we can rewrite the equation as:
n^2 + n - 12 = (n + ?)(n + ?)
Now we need to find two numbers that satisfy the aforementioned conditions. The product of these two numbers should be -12, and their sum should be 1.
After some trial and error, we can find that 4 and -3 satisfy these conditions. Therefore, we can factor the equation as follows:
n^2 + n - 12 = (n + 4)(n - 3)
Now, using the zero product property, we can set each factor equal to zero and solve for n:
n + 4 = 0 --> n = -4
n - 3 = 0 --> n = 3
So the solutions to the equation n^2 + n - 12 = 0 are n = -4 and n = 3.