Question

Check weather 6x2-5x - 14 is exactly divisible by (x-2) or not

Answer 1

Answer: Yes: divisible

Explanation:

`P(x)=6x^2-5x-14\\\\P(2)=6*2^2-5*2-14=24-10-14=0\\\\P(x)\ is\ exactly\ divisible\ by\ x-2\\`

Answer 2

`\large \boldsymbol {} 6x^2 -5x-14 =0 \\\\ D=25+14\cdot 4\cdot 6 =361=19^2 \\\\ x_1= (5+19)/(12) =2 \\\\\\ x_2 =(5-19)/(12) =-(7)/(6) \\\\ and \ \ we \ \ \ know \ \ that \\\\\ 6x^2 -5x-14 =6 (x-x_1) ( x- x_ 2) = 6 ( x-(-(7)/(6) ))\boldsymbol { ( x-2 ) } \\\\ as \ we \ can \ see \ , \ the \ \ expansion \ is \\\\\ x-2 ; therefore \ \ , \ \ the \ \ answer \ \ is \ \ yes`