Question

solving quadratic equations: zero product property

a quadratic equation has the solutions \\(x = -4\\) and \\(x = -7\\).

write a possible quadratic equation in standard form.

enter your answers in the boxes.

\\(x^2 + \square x + \square = 0\\)

Explanation:

Write the factored form of the quadratic equation

$$ (x - (-4))(x - (-7)) = 0 $$

$$ (x + 4)(x + 7) = 0 $$

Expand the factors to standard form

$$ x^2 + 7x + 4x + 28 = 0 $$

$$ x^2 + 11x + 28 = 0 $$

Identify the coefficients for the boxes

$$ x^2 + 11x + 28 = 0 $$

Answer:

A quadratic equation has the solutions \(x = -4\) and \(x = -7\).

Write a possible quadratic equation in standard form.

Enter your answers in the boxes.

\(x^2 +\) <blank>11</blank> \(x +\) <blank>28</blank> \(= 0\)