Answer:
Option D: x = -2; x = 3/4
Step-by-step explanation:
Hello!
We can factor this expression and then find the zeroes to find our solutions.
Factor:
We have to factor by grouping. Multiply the 1st and last term, 4x² and -6 is -24x², and find two factors that equal to -24x² and add up to the second term, 5x. 8x and -3x work for this.
- y = 4x² + 5x - 6
- y = 4x² + 8x - 3x - 6
- y = 4x(x + 2) - 3(x + 2)
- y = (4x - 3)(x + 2)
Zero-Product Property
Now, set the equation equal to zero.
Remember, if two numbers, a and b, multiply to 0, either a or b or both numbers must be zero. So now we set both factors to zero, hence the zero-product property.
And the next one:
The solutions are x = -2, and x = 3/4, or Option D
