Final answer:
A quadratic equation with the solutions 1 and -7 is written as (x - 1)(x + 7) = 0. Expanding this, we get x² + 6x - 7 = 0, which is the standard form of a quadratic equation with those solutions.
Step-by-step explanation:
To write a quadratic equation with the solutions 1 and -7, we use the fact that if p and q are solutions to a quadratic equation, then the equation can be written as (x - p)(x - q) = 0. Therefore, with the solutions 1 and -7, we can write the equation as (x - 1)(x + 7) = 0. To develop this into a standard quadratic equation of the form ax² + bx + c = 0, we simply expand the brackets.
(x - 1)(x + 7) = 0
x² + 7x - x - 7 = 0
x² + 6x - 7 = 0
So the quadratic equation is x² + 6x - 7 = 0.