Question

3x^2 -5x -2=0

Answer 1

Answer:

Step-by-step explanation:

1. Find two numbers that add to make the coefficient of x (in this case, -5) and that multiply to make the constant term multiplied by the coefficient of x^2 (in this case, -2 x 3 = -6)

Two numbers that work are -6 and +1

-6 x +1 = -6

-6 + -1 = -5

2. Split the middle term into the two numbers that you found.

3x^2 -6x +x -2 = 0

I've put the -6 on the left side because in our next step, when we factorise, it will be easier than having the numbers the other way around.

3. Factorise the left side by taking out common factors from each pair. The pairs I'm talking about here are '3x^2 and -6x', and 'x and -2'

3x (x-2) +1 (x-2) = 0

4. You now have two numbers both being multiplied by the term x-2. We can rearrange this equation to give us two brackets being multiplied by each other.

(3x + 1) (x-2) = 0

5. According to the Null Factor Law, if two terms are multiplied together and the result is 0, then one of those terms must be 0. Make both terms equal to 0 and solve each for x.

3x + 1 = 0              x-2 = 0

3x = -1                   x = 2

x = -1/3

6. The solutions to this equation are x = 2 and x = -1/3

Answer 2

Answer:

Step-by-step explanation:

Start by separating (not factoring) -5x.  For example, we might get {-2x, - 3x} (note how these combine to produce -5x).  Might have to try several combinations to find the right one.

Then 3x^2 -5x -2=0 could possibly be x(3x - 2) - (3x - 2), or

                                                                x(3x - 2) - 1(3x - 2).

Notice how the factor (3x - 2) shows up twice.  If we factor out (3x - 2) we are left with (x - 1).  We check these results by multiplying (3x - 2) and (x - 1) together, so we can be sure that the result is the original 3x^2 -5x -2=0.

(3x - 2)(x - 1) = 3x^2 - 3x - 2x + 1 results in 3x^2 - 5x + 2.  Unfortunately, the sign of that 2 is incorrect; we'd hoped for -2, not +2.

To check this further, I used synthetic division with 1 as divisor; the remainder is -4, which tells us that (x - 1) is not a factor of 3x^2 -5x -2=0.

Please double check to ensure that you have copied this problem down correctly.