Question

2x^2 + 16x + 28 = 0?

Answer 1

`x=-4+√(2)`

`x=-4-√(2)`

Explanation:

The quadratic formula is an equation that can be used to find the roots of a quadratic equation when one is given the equation in standard form. A quadratic equation in standard form is the following,

`ax^2 +bx + c=0`

The quadratic formula is the following,

`((-a)(+-)√((x)^2-4(b)(c)))/(2(a))`

Substitute in the given coefficients for the following equation,

`2x^2 + 16x + 28 = 0`

Substitute,

`(-16(+-)√((16)^2-4(2)(8)))/(2(2))`

Simplify,

`(-16(+-)√(256-224))/(4)\\\\=(-16(+-)√(32))/(4)\\\\=(-16(+-)4√(2))/(4)\\\\=-4(+-)√(2)`

The roots of the quadratic equation (
`2x^2+16x+28=0`) are (
`x=-4+\sqrt2`) and (
`x=-4-√(2)`)