2x2 - 3x - 2 = 0 can be factored as
(2x + 1)(x - 2) = 0
So, the roots of the quadratic are the solutions of
2x + 1 = 0 (set one of the factors = 0)
2x = -1 (subtract 1 from both sides)
x = -1/2 (divide both sides by 2)
And
x - 2 = 0 (set the other factor = 0)
x = 2 (add 2 to both sides)
____
You can also solve this using the quadratic formula. It will give the same answers.
To arrive at these factors, you can recognized that the factors of each of the coefficients having a value of 2 must be 1 and 2. We recognize that multiplying 2*2 and subtracting 1*1 will give 3, so we suspect that with appropriate choice of signs we can make factors that look like (±2x±1)(±1x±2) multiply out to the given equation. It took me a couple of trials to arrive at the factors shown above.
(2x + 1)(x - 2) = 0
So, the roots of the quadratic are the solutions of
2x + 1 = 0 (set one of the factors = 0)
2x = -1 (subtract 1 from both sides)
x = -1/2 (divide both sides by 2)
And
x - 2 = 0 (set the other factor = 0)
x = 2 (add 2 to both sides)
____
You can also solve this using the quadratic formula. It will give the same answers.
To arrive at these factors, you can recognized that the factors of each of the coefficients having a value of 2 must be 1 and 2. We recognize that multiplying 2*2 and subtracting 1*1 will give 3, so we suspect that with appropriate choice of signs we can make factors that look like (±2x±1)(±1x±2) multiply out to the given equation. It took me a couple of trials to arrive at the factors shown above.
