Question

Determine the zeros of the function y= 2x² + 12x + 22

Answer 1

zeros of the function y=
`2x^2 + 12x + 22` is
`x = -3+( √(8)i )/(2)` &
`x = -3-( √(8)i )/(2)`.

Explanation:

Here we have , y=
`2x^2 + 12x + 22` in order to find zeros of this quadratic function we get:
`2x^2 + 12x + 22 = 0`

⇒
`2x^2 + 12x + 22 = 0`

⇒
`x^2 + 6x + 11 = 0`

⇒
`x = (-b \pm √(b^2-4a(c)) )/(2a)`

⇒
`x = (-(6) \pm √(6^2-4(1)(11)) )/(2(1))`

⇒
`x = (-6 \pm √(36-44)) )/(2)`

⇒
`x = (-6 \pm √(8)i )/(2)`

⇒
`x = -3 \pm ( √(8)i )/(2)`

Since, we have two root one with positive & other with negative sign so :

⇒
`x = -3-( √(8)i )/(2)`

Therefore, zeros of the function y=
`2x^2 + 12x + 22` is
`x = -3+( √(8)i )/(2)` &
`x = -3-( √(8)i )/(2)`.