Question

Please help with this Math Question...

Answer 1

Answer: A

Explanation:

f(x) = x³ + 4x² + 7x + 6

possible rational roots are ±{1, 2, 3, 6}

Try x = -2

-2 | 1 4 7 6

| ↓ -2 -4 -6

1 2 3 0 ← remainder is 0 so x = -2 is a root ⇒ (x + 2) = 0

The factored polynomial x² + 2x + 3 = 0 is not factorable so use the quadratic formula to find the roots.

a=1, b=2, c=3

`x=(-b\pm√(b^2-4ac) )/(2a)`

`x=(-(2)\pm√((2)^2-4(1)(3)) )/(2(1))`

`x=(-2\pm√(4-12) )/(2)`

`x=(-2\pm√(-8) )/(2)`

`x=(-2\pm2i√(2))/(2)`

`x = -1 \pm i√(2)`

`x = -1 + i√(2)`
`x = -1 - i√(2)`

`x - (-1 + i√(2))=0`
`x - (-1 - i√(2))=0`

The factors are:

`(x - 2)[x - (-1 + i√(2))][x - (-1 - i√(2))]`