Question

What are the solutions to the equation y = 4x2 +5x−6?

Answer 1

Option D: x = -2; x = 3/4

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.

• 0 = (4x - 3)(x + 2)

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.

• 4x - 3 = 0
• 4x = 3
• x = 3/4

And the next one:

• x + 2 = 0
• x = -2

The solutions are x = -2, and x = 3/4, or Option D