Question

What are the solutions of the equation?

6x^2 + 11x + 4 = 0

a. 4/3, 1/2
b. -4/3, -1/2
c. 4/3, -1/2
d. -4/3, 1/2

Answer 1

Answer:

Correct option is b; $x= \frac{-4}{3},\frac{-1}{2}$

Step-by-step explanation:

Given equation 6x² + 11x + 4 = 0

Using factorization method to solve it

6x² + 8x + 3x + 4 = 0

Dividing the central term into two terms in such a way that their product gives 24x² and their sum gives 11x

taking common in the above equation

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

taking 3x+4 common

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

we can write from eq1

(3x+4) = 0

3x = -4

$x= \frac{-4}{3}$

and we can write from eq1

2x+1 = 0

2x = -1

$x= \frac{-1}{2}$

Answer 2

Answer:

b. -4/3, -1/2

Step-by-step explanation:

We are given the following equation and we are to solve it by factorizing it:

$6x^2 + 11x + 4 = 0$

We are to find factors of 24 such that when multiplied they give a product of 24 and when added they give a result of 11.

$6x^2+3x+8x+4=0$

$3x(2x+1)+4(2x+1)=0$

$(2x+1)(3x+4)=0$

$2x+1=0, 3x+4=0$

$x=-\frac{1}{2} , x=-\frac{4}{3}$

Therefore, the correct answer option is b. -4/3, -1/2.