Question 473448
<br>Standard form of a quadratic equation is:
ax<sup>2</sup> +  bx + c = 0, where a, b and c are some constants.<br>
If we are given solutions to a quadratic equation as x<sub>1</sub> and x<sub>2</sub>, then these solutions must satisfy the following quadratic equation:
(x - x<sub>1</sub>)(x - x<sub>2</sub>) = 0<br>
If 7 is the only solution to a quadratic equation, this means that both solutions, 
x<sub>1</sub> and x<sub>2</sub> happened to be the same number, which is 7.
Hence, a quadratic equation whose only solution is 7 can be written as:
(x - 7)(x - 7) = 0, 
which can be transformed into standard form by expanding the brackets and simplifying.<br>
The resulting equation is:
x<sup>2</sup> - 14x + 49 = 0
This quadratic equation is one possible answer to your question.<br>
However, the are infinite number of quadratic equations whose only solution is 7.
The class of these equations can be described as:
kx<sup>2</sup> - 14kx + 49k = 0,
where k is any real number.