Question 473448: If 7 is the only solution to a quadratic equation, then how would I write it in standard form?
Answer by karaoz(32)   (Show Source):
You can put this solution on YOUR website!
Standard form of a quadratic equation is:
ax2 + bx + c = 0, where a, b and c are some constants.
If we are given solutions to a quadratic equation as x1 and x2, then these solutions must satisfy the following quadratic equation:
(x - x1)(x - x2) = 0
If 7 is the only solution to a quadratic equation, this means that both solutions,
x1 and x2 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.
The resulting equation is:
x2 - 14x + 49 = 0
This quadratic equation is one possible answer to your question.
However, the are infinite number of quadratic equations whose only solution is 7.
The class of these equations can be described as:
kx2 - 14kx + 49k = 0,
where k is any real number.
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