Question

Which equation is true for x = –6 and x = 2?

2x2 – 16x + 12 = 0
2x2 + 8x – 24 = 0
3x2 – 4x – 12 = 0
3x2 + 12x + 36 = 0

Answer 1

Second statement 2x2 + 8x – 24 = 0 Is true for the given conditions. When x = -6 2x2 + 8x – 24 = 0 Becomes 2(-6)2 + 8(-6) – 24 = 0 2(36) - 48 - 24 = 0 72 - 48 - 24 = 0 0 = 0 Which is true. When x = 2 2x2 + 8x – 24 = 0 Becomes 2(2)2 + 8(2) – 24 = 0 2(4) + 16 - 24 = 0 8 + 16 - 24 = 0 0 = 0 Which is true. So 2x2 + 8x – 24 = 0 will be answer.

Answer 2

we know that

using a graph tool

let's proceed to graph each case to determine the roots

case 1)
`2x^(2) - 16x + 12 = 0`

the roots are

`x1=0.8\ x2=7.2` ------> is not the solution

see the attached figure N
`1`

case 2)
`2x^(2) +8x -24 = 0`

the roots are

`x1=-6\ x2=2`

see the attached figure N
`2` --------> is the solution

case 3)
`3x^(2) - 4x - 12 = 0`

the roots are

`x1=-1.4\ x2=2.8`------> is not the solution

see the attached figure N
`3`

case 4)
`3x^(2) +12x +36 = 0`

the graph does not have x-intercepts

see the attached figure N
`4` ------> is not the solution

therefore

the answer is

the solution is

`2x^(2) +8x -24 = 0`