ok then umm How was your day?:D
Answer:
a = 4, b = - 5, c = 5
Step-by-step explanation:
Expand the product of factors on the left side and compare like terms on both sides.
(3x - 1)(ax + b) ← expand using FOIL
= 3ax² + 3bx - ax - b
= 3ax² + (3b - a)x - b
Equating coefficients of like terms with 12x² - 19x + c , then
3a = 12 ( divide both sides by 3 )
a = 4
3b - a = - 19
3b - 4 = - 19 ( add 4 to both sides )
3b = - 15 ( divide both sides by 3 )
b = - 5
c = - b = - ( - 5) = 5
By definition, rational numbers are ratios between integer numbers:
![\mathbb{Q} = \left\{\dfrac{a}{b}:\ a,b\in\mathbb{Z},\ b\neq 0\right\}](https://tex.z-dn.net/?f=%20%5Cmathbb%7BQ%7D%20%3D%20%5Cleft%5C%7B%5Cdfrac%7Ba%7D%7Bb%7D%3A%5C%20a%2Cb%5Cin%5Cmathbb%7BZ%7D%2C%5C%20b%5Cneq%200%5Cright%5C%7D%20)
So, you get every possible rational number by dividing two integer numbers.