Factoring Problem with 12

[Jason76]

\(\displaystyle x^{2} - x - 12\)

What two numbers have a product of \(\displaystyle -12\) and a sum of \(\displaystyle -1\)

 

[Deleted member 4993]

\(\displaystyle x^{2} - x - 12\)

What two numbers have a product of \(\displaystyle -12\) and a sum of \(\displaystyle -1\)

by observation: 3 and -4

by algebra:

a + b = -1..................................................(1)

ab = -12

(a-b)² = (a+b)² - 4ab = 1 + 48 = 49 → a - b = ± 7

combining with equation (1)

(a,b) = (3 , -4) or (-4,3)

 

[Jason76]

by observation: 3 and -4

by algebra:

a + b = -1..................................................(1)

ab = -12

(a-b)² = (a+b)² - 4ab = 1 + 48 = 49 → a - b = ± 7

combining with equation (1)

(a,b) = (3 , -4) or (-4,3)

Right, sounds good.