Solve f(x) = 2x^2 -x -15 by factoring.

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Given the function f(x) = 2x^2 -x -15

We need to solve for x by factoring.

First we have a quadratic equation. Then we can simplify into two factor.

==> f(x) = 2x^2 -x -15

We will try and determine one of the roots.

We will substitute with x=3.

==> f(3) = 2*9 0-3 -15 = 0

==> X=3 is one of the roots.

Then (x-3) is one of the factor.

==> f(x) = (x-3) * R(x)

Now, to find the other factor, we will divide f(x) by (x-3).

**==> f(x) = (x-3)(2x+5)**

**==> x1= 3 **

**==> x2= -5/2**

We have to solve f(x) = 2x^2 -x -15 by factoring.

Now we see that -1 can be written as 5 - 6 = -1. Here 5*-6 = -30.

f(x) = 2x^2 -x -15 = 0

=> 2x^2 - 6x + 5x - 15 = 0

=> 2x(x - 3) + 5(x - 3) = 0

=> (2x + 5)(x - 3) = 0

For 2x + 5 = 0

=> x = -5/2

And for x - 3 = 0

=> x= 3

**Therefore x is equal to -5/ 2 and 3.**

-5/ 2 and 3.

The equation 2x^2 -x -15 = 0 has to be solved for x.

The solution of a quadratic equation ax^2 + bx + c = 0 is given by the formula:

`(-b+-sqrt(b^2 - 4ac))/(2a)`

Here, a = 2, b = -1 and c = -15

Substituting these values in the formula gives:

`(-(-1)+-sqrt((-1)^2 - 4*2*-15))/(2*2)`

= `(1 +-sqrt(1 +120))/(4)`

= `(1 +-sqrt(121))/(4)`

= `(1 + 11)/(4)` and `(1 - 11)/4`

= 12/4 and -10/4

= 3 and -5/2

The roots of 2x^2 -x -15 = 0 are x = 3 and x = -5/2

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