Question

Use the equation x 2 −7x+6 = 0 to answer all of the following questions.

Answer 1

Part A: -6 and -1

Part B: (x - 6)(x - 1) = 0

Part C: x = 6 and x = 1

Explanation:

We need to find two numbers that add up -7 and multiply to 6.

We know that 6 * 1 = 6, but 6 + 1 is not -7. However, -6 * -1 = 6 and -6 + -1 = -7. Our factors are -6 and -1.

Next, we will rewrite this in factored form. Using the factors above, the form is as follows.

(x - 6)(x - 1) = 0

Lastly, we will use the zero product property to solve. This states that if xy = 0, then x = 0 and y = 0 because anything times zero is equal to zero.

x - 6 = 0 x - 1 = 0

x = 6 x = 1