Answer:
x² + 49 = 0
Explanation:
An equation with the form (x - a)(x - b)= 0 has as a solutions x = a and x = b.
In this case, the solutions are x = 7i and x = -7i, so the equation will be:
(x - 7i)(x - (-7i)) = 0
(x - 7i)(x + 7i) = 0
Now, we need to apply the distributive property, so:
x(x) + x(7i) - 7i(x) - 7i(7i) = 0
x² + 7xi - 7xi - 49i² = 0
x² - 49i² = 0
Since, i² = -1, we get:
x² - 49(-1) = 0
x² + 49 = 0
Therefore, the quadratic equation in standard form is:
x² + 49 = 0
