I need help with a polynomial problem. Simple algebra problem.?

Question

What the easiest way to solve this for x? I always run into problems when i go about solving a polynomial with a number in the front of them....please help!

2x^2 - 5x - 3

thank you.

Answer 1

Well, if the 2 in front of the x² is bothering you, divide the whole thing by 2:

x² - (5/2) x - (3/2) = 0

You end up with some fractions, but at least there's no 2. Both equations have the same solutions. Here are the factors:

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

As you can see, both end up with x = 3 and x = -1/2. The quadratic formula will also work to the same end:

for the equation a*x² + b*x + c = 0,
x = [-b ± √(b² - 4*a*c)]/[2*a]

plugging in the values for a, b, and c:

x = [-(-5) ± √(5² - 4*2*(-3))]/[2*2]
x = [5 ± √(25 + 24)]/[4]
x = [5 ± √(49)]/[4]
x = [5 ± 7]/[4]
x = [5 + 7]/[4] or x = [5 - 7]/[4]
x = 12/4 or x = -2/4
x = 3 or x = -1/2
OR
x = [-(-5/2) ± √((5/2)² - 4*(1)*(-3/2))]/[2*1]
x = [5/2 ± √(25/4 + 12/2)]/[2]
x = [5/2 ± √(49/4)]/[2]
x = [5/2 ± 7/2]/[2]
x = [5/2 + 7/2]/[2] or x = [5/2 - 7/2]/[2]
x = [12/2]/[2] or x = [-2/2]/[2]
x = 3 or x = -1/2

So, whatever works for you! Hope that helps.

Answer 2

That isn't an equation, it isn't set to equal (=) anything. Assuming you mean that you want to factor it:

The answer is (2x+1)(x-3). I came to this by realizing -3 x 2 = -6 and then +1 gets -5 which is the center coefficient. What you want to do is think of the factors of -3 in your head and then how you can multiply those with the factors of 2 followed by adding them to get -5.

I find the quickest way is really to just imagine the factors and then do a kind of elimination in your head. -3, +1 are factors of 3 and then 2, 1 are factors of 2. Multiply -3 and 2 to get -6 and then 1 and 1 to get 1 which added is -5.


P.S. in a problem like this with relatively small numbers this is definitely the fastest way, I did this in about 3 seconds.

Answer 3

In the equation ax^2 + bx + c, the roots are equal to

(-b +/- sqrt(b^2 - 4 * a * c)) / 2a

In this problem:

a = 2
b = -5
c = -3

(- (-5) +/- sqrt((-5)^2 - 4 * 2 * -3)) / 2 * 2

(5 +/- sqrt (25 + 24)) / 4

(5 +/- sqrt (49)) / 4

(5 +/- 7) / 4

12/4 or -2/4
3 or -1/2

(x - 3)(2x + 1)

Answer 4

Assuming it's equal to zero, you can factor by FOIL. You know the two factors start with 2x and 1x, and the signs are + and - because the last number is negative, so by trial and error you'll get it.

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

Then make each factor = 0 and solve.

2x + 1 = 0; 2x = -1; x = -1/2

like that

Answer 5

interior the 1st case, invert the 2d fraction and multiply you are able to desire to component first, so as which you will cancel 8 over x^4(x-4) cases x^5 over 4(x+4) cancel the 8 and the 4 to be 2 and a million cancel x^4 to be a million and x Now you have 2 over (x-4) cases x over x+4 Multiply to get 2x over (x-4)(x+4) or 2x over x^2 -sixteen interior the 2d case, cancel the x-3 components and the x+7 components to get a million/(x+3) cases (x+7) over (x+2) (x+7) over (x+3)(x+2)

Answer 6

Hi..
i already posted a picture of ur question with a worked solution at http://www.icedor.com under Elementary Maths Forum under Algebraic Manipulation. the answer i gave is labeled.. Factorisation Method

You said u have problems wif factorisation.. this method will help!!

http://www.icedor.com/icedoronline/course/index.php?cid=FLM101

Answer 7

2 x^2 - 6x +x -3 = 2x(x-3) + (x-3)= (x-3) ( 2x+1)

x1= 3
x2= -1/2

Answer 8

Try using the quadratic formula for equations that don't factor easily.