Use the zero product property to find the solutions to the equation x² + 12 = 7x.

The zero product property is nothing but if ab = 0 ⇒ either a = 0 or b = 0 or both a and b are equal to zero. 

Answer: x = 3 or x = 4 are the solutions of the given quadratic equation x² + 12 = 7x, obtained by using the zero product property.

Let us use the zero product property to find the solutions to the given equation.

Explanation:

We inherently use the zero product property in solving the quadratic equations in the factorization method by splitting the middle term.

x² + 12 = 7x

x² - 7x + 12 = 0

x² - 4x - 3x + 12 = 0 -------------> splitting the middle term

x(x - 4) - 3(x - 4) = 0

(x - 4) (x - 3) = 0

either (x - 4) = 0 or (x - 3) = 0 or both (x - 4) & (x - 3) -------------> application of zero product property

(x - 4) = 0 ⇒ x = 4

or,

(x - 3) = 0 ⇒ x = 3

Thus, x = 3 or x = 4 are the solutions of the given quadratic equation x² + 12 = 7x.