What are the solutions of the equation?
2 answers:
Answer:
Correct option is b;
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
and we can write from eq1
2x+1 = 0
2x = -1
<u>Answer:</u>
b. -4/3, -1/2
<u>Step-by-step explanation:</u>
We are given the following equation and we are to solve it by factorizing it:
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.
Therefore, the correct answer option is b. -4/3, -1/2.
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You can get all the terms on one side, and then solve for x by any means:
Factor out a -2:
Factor this equation:
I will use the AC method. To use it, first multiply a and c (in ax^2 + bx +c):
Now, look for two numbers that multiply to -12 and add to -11. Obviously these numbers are -12 and 1. (-12*1 = -12 and -12+1 = -11). Now, because of rules, you set it up in a Punnett square:
4x^2 -12x
x -3
Now, we find common factors of the terms in rows:
_x_______-3__
4x| 4x^2 -12x
1 | x -3
So, you can use this to write an equivalent expression to the quadratic given:
Now, we known the factors are (solve for x): 3 and -1/4.
Factor out a -2:
Factor this equation:
I will use the AC method. To use it, first multiply a and c (in ax^2 + bx +c):
Now, look for two numbers that multiply to -12 and add to -11. Obviously these numbers are -12 and 1. (-12*1 = -12 and -12+1 = -11). Now, because of rules, you set it up in a Punnett square:
4x^2 -12x
x -3
Now, we find common factors of the terms in rows:
_x_______-3__
4x| 4x^2 -12x
1 | x -3
So, you can use this to write an equivalent expression to the quadratic given:
Now, we known the factors are (solve for x): 3 and -1/4.