Quadratic equation?

Question

How do you factorise this?(and how did you get there?)

4x^2+4x-3=0

Answer 1

4x² + 4x + 3 = 0

4x² + 6x - 2x + 3 = 0

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

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

- - - - - - - - - -s-

Answer 2

I am afraid that a lot of trial and error is involved

Possible answers are

(4x + a)(x + b) then a x b = -3 this gives possible values of a = 3, -3 , 1 or -1 and the corresponding b = -1, 1, -3 or 3

Each of these pairs must be checked to see if they give your equation

(4x +3)(x - 1) = 4x^2 - x - 3
(4x -3)(x + 1) = 4x^2 + x -3
(4x + 1)(x - 3) = 4x^2 - 11x -3
(4x - 1)(x + 3) = 4x^2 + 11x - 3

and as this hasn't worked you would have to try

(2x + c)(2x + d)

(2x + 3)(2x - 1) = 4x^2 + 4x - 3
(2x - 3)(2x + 1) = 4x^2 - 4x - 3

So (2x + 3)(2x - 1) = 0 is the factorised version

and x = -3/2 or x = 1/2 are the solutions

Answer 3

4x^2 + 4x - 3 = 0
(2x + 3)(2x - 1) = 0

Essentially, you're looking for a combination of factors from the leading term and final constant that will also provide you the correct middle coefficient. The signs between the terms also given you a hint. If the final constant is -3, then the two numbers that multiply together to give you this number must be of opposite signs. You know that the factors of 4, the leading cofficient are 4 x 1 and 2 x 2, while the factors of -3, the constant, are -3 x 1 or 3 x -1. Just by trial and error, you can try various combinations until you find the one that works perfectly.

Answer 4

(2x + 3).(2x - 1) = 0
x = - 3/2 , x = 1/2
Method used is trial and error:-
Start with 4x² which could have factors of 2x and 2x or 4x and x
Factors of - 3 are 3 and -1 or 1 and - 3.
Check
(2x) x (2x) = 4x² as required
3 x - 1 = - 3 as required.
- 2x + 6x = 4x as required.
Keep practising----you`ll make it!
Good luck.

Answer 5

a = 4
b = 4
c = - 3
ac = -12

think of two numbers which give a sum of 4(=b)
and whose product is -12 (=ac)

by trial and error the numbers are -2 and 6

break up the middle term

4x^2-2x+6x -3=0

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

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

x = (1/2) , (-3/2)

Answer 6

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

look at the first number 4x^2
what goes into it is either (2x)(2x) or (4x)(1x)

lets try the 2x

(2x )(2x )

The last number is (-) so that means that the signs are opposite

(2x + )(2x - )

now look at the last number 3
that is simply (3)(1)
Since the middle number is a positive, that means that the largest product (either the outside 2 or the inside 2) is positive

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

Double check your answer
F (2x)(2x) = 4x^2
O (2x)(-1) = -2x
I (2x)(3) = 6x
L ((3)(-1) = -3

There you go!!

Answer 7

its the factors of the last number (three is the last number) multiplied by factors off 4x². 3 and 1 are factors of 3. 2x and 2x are factors of 4x².iif one is negative and the other is positve then both bractets are negative like this (2x-1)(2x-3)

Answer 8

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

To check, FOIL (2x - 1)(2x + 3) = 4x^2 + 6x - 2x - 3 = 4x^2 + 4x - 3. Yep. Checked good.

Answer 9

4x^2+4x-3=0
4x^2-2x+6x-3=0
2x(2x -1)+3(2x -1) =0
(2x + 3) (2x - 1) =0
x1=(-3/2)
x2=(1/2)

hope can help u..
thanks

Answer 10

use the quadratic formula to solve for x.

-b (+/-)V((b^2)-4ac)/2a (where V is a square root sign)

a = 4, b = 4, c=-3

then you take these values for x and invert them and put them in brackets! (x+x1)(x+x2) where x1 and x2 are youre inverted calculated values of x