Answer + explanation of steps:

We have:

`f(x) = ax^2 - x + b` `(a ne 0)`

`-` Highest coefficient : `a` (because `x^2` is the degree of the polynomial)

`-` The coefficient of freedom : `b` 

And : `a + b = -7`

`=> b = -7 - a`

Substitute the solution `x = 2` and `f(x) = 0` :

`a . 2^2 - 2 + b = 0`

`=> 4a - 2 + b = 0`

`=> 4a - 2 + (-7 - a) = 0`

`=> 4a - 2 - 7 - a = 0`

`=> 3a - 9 = 0`

`=> 3a = 9`

`=> a = 3`

`@` `a + b = -7`

`=> 3 + b = -7`

`=> b = -10`

Conclusion : so `a = 3 ; b = -10`

$-$ The polynomial `f(x) = ax^2 - x + b` has the solution `x = 2 `

`=> a. 2^2 - 2 + b = 0 `

`<=> 4a - 2 + b = 0 `

`<=> 4a + b = 2     ( 1 )`

$-$ The sum of the highest coefficient and the coefficient of freedom of `-7 `

`=> a + b = -7     ( 2 )`

From `( 1 )` and `( 2 ) :`

`=> {( 4a + b = 2 ),( a + b = -7 ):}`

`<=> {( 4a + b = 2 ),( b = -7 - a ):}`

`<=> {( 4a + ( -7 - a ) = 2 ),( b = -7 - a ):}`

`<=> {( 4a - 7 - a = 2 ),( b = -7 - a ):}`

`<=> {( 4a - a = 2 + 7 ),( b = -7 - a ):}`

`<=> {( 3a = 9 ),( b = -7 - a ):}`

`<=> {( a = 3 ),( b = -7 - 3 ):}`

`<=> {( a = 3 ),( b = -10 ):}`

  So `( a ; b ) = ( 3 ; -10 )`