Question

Solve these


`{x}^(2) - 5x + 6`

`{x}^(2) - 11x + 28`
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Answer 1

hope this will help you more

Answer 2

`x^2-5x+6`

x = 3, x = 2

`x^2-11x+28`

x = 7, x = 4

Explanation:

One is asked to solve two quadratic equations. Both of these quadratic equations are in standard form. This means that the two equations follow the following general format;

`ax^2+bx+c`

The quadratic formula is a method of solving a quadratic equation using the coefficients of the terms in the equation. The quadratic equation is the following,

`(-b(+-)√(b^2-4ac))/(2a)`

Substitute in each of the terms and solve for the roots in each equation;

`x^2-5x+6`

Substitute, and solve

`(-(-5)(+-)√((-5)^2-4(1)(6)))/(2(1))\\\\=(5(+-)√(25-25))/(2)`

`=(5+1)/(2)`
`=(5-1)/(2)`

`=3`
`=2`

`x^2-11x+28`

Substitute, and solve

`(-(-11)(+-)√((-11)^2-4(1)(28)))/(2(1))\\=(11(+-)√(121-112))/(2)`

`=(11+√(9))/(2)`
`=(11-√(9))/(2)`

`=(11+3)/(2)`
`=(11-3)/(2)`

`=7`
`=4`