Answer:
E. x = 1/2
F. x = -4/3
Step-by-step explanation:
The given equation is
6x² + 5x - 4 = 0
To find the solution, we need to factorize the polynomial, so we will use the divide and slide method.
First, multiply the coefficient of x², in this case, it is 6, by the constant, which is -4, and rewrite as
x² + 5x - 4(6)
x² + 5x - 24
Now, we need to find two numbers that multiply to -24 and add to 5. These numbers are 8 and -3, so
(x + 8)(x - 3)
Finally, divide the constants by 6 and simplify
(x + 8/6)(x - 3/6)
(x + 4/3)(x - 1/2)
And slide the denominator as a coefficient of x, so
6x² + 5x - 4 = (3x + 4)(2x - 1)
Therefore, the initial equation is
(3x + 4)(2x - 1) = 0
Now, this is equal to 0 if one of the factors is equal to 0, so the solutions of the equation are
3x + 4 = 0
3x = -4
x= -4/3
2x - 1 = 0
2x = 1
x = 1/2
Then, the answers are:
E. x = 1/2
F. x = -4/3