quadratic stuff please show work please and thank you

Question

Two numbers have a sum of 1 and a product of -6 use the quadratic equation -n*2+n+6=0 to determine the two numbers

please and thank you

Answer 1

Step 1: For factoring quadratics, I always look at the last term first. What are the factors that when multiplied together add up to the last term?

In this case, they are (1 and 6) and (2 and 3). We also know that since the sign in front of the last term is positive, this means that either both of the pair of factors have to be both negative or both positive. If the sign were negative, this would mean that one is negative and the other is positive.

Step 2: Then I look at the first term. (I am assuming you mean negative n squared, which is better written as -n^2 or -n².) What factors of n would equal -n²? (n and -n).

Step 3: Look at the middle term to offer guidance on which factors are the right ones. Since the middle term in +n, this means that sum of the "n-terms" is positive and the difference between the terms is one. This would make me look at the second pair in Step 1 is probably the right choice, because if one n-term is positive and the other negative, there would only be 1 n difference, which is what is in the question you asked. Since from Step 2, we know that one n is negative and the other positive, we should multiply the negative n times the smaller of the factors so that the sum remains positive.

(n + 2)(-n + 3)

Step 4: To double check, we should use the FOIL method to ensure we got what we started with.

First: n * - n = -n²

Outer: n * +3 = 3n

Inner -n * +2 = -2n

Last: +2 * +3 = 6

-n² - n + 6 <== looks good.

Step 5: To find the solution, we set each solution to zero and solve.

n + 2 = 0 ==> n = -2

-n + 3 = 0 = n - 3 = 0 ==> n = 3

Answer 2

The equation you have given is NOT correct.

x + y =1

xy = -6

x(1-x) = -6

x² - x -6 = 0

(x+2)(x-3) = 0

x = 3 and y = -2 (or vice versa).