Question

Actual roots of f(x)=2x^2+2x-24

Answer 1

x= 3, -4

Explanation:

Set 2 x ² + 2 x − 24 equal to 0 .

2 x ² + 2 x − 24 = 0

Solve for x .

Factor the left side of the equation.

2 ( x² + x − 12 ) = 0

Factor

x ² + x − 12 using the AC method.

2 ( x − 3 ) ( x + 4 ) = 0

If any individual factor on the left side of the equation is equal to 0 , the entire expression will be equal to 0 .

x − 3 = 0

x + 4 = 0

Add 3 and subtract 4 to both sides of the equation.

x = 3

x = -4

Answer 2

`f(x) = 2 {x}^(2) + 2x - 24`

`f(x) = 2( {x}^(2) + x - 12)`

`0 = 2( {x}^(2) + x - 12)`

Divided sides by 2

`{x}^(2) + x - 12 = 0`

`(x + 4)(x - 3) = 0`

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`x + 4 = 0`

`x = - 4`

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`x - 3 = 0`

`x = 3`

Thus the actual roots are -4 and 3.....

And we're done.

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