Question

Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form.

ax^2 +bx +c=0
7 is the only solution.
The equation is _=0

Answer 1

If 7 is the only solution, and you want a quadratic function (a function that must have 2 solutions), 7 must be whats called a double root. There are a couple of ways to do this.

One way (the most straightforward, not the easiest though) is to multiply this out:
(x - 7)(x - 7)

Another way (easier) is to know that if you have the roots of a polynomial, just add them, and multiply them, and that gives you the function.

I want both roots to be 7.
7 + 7 = 14
7*7 = 49

so my answer is \[x^2-14x+49\]

Answer 2

i guess i should be a little more specific, if you have the roots of a Quadratic polynomial, just add the root, and multiply them, and those numbers lead to your solution.

Answer 3

More examples:

I want a quadratic polynomial whose roots are 3 and -10

3+ (-10) = -7
3*(-10) = -30

answer is:
\[x^2+7x-30\]