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
The Solution is 10, only solution!
(x10)(x-10)=0
x^2-20x+100=0
The answer is correct.
In fact, the "only" solution is 10 means that there are two coincident solutions which are both 10. You have used the information correctly to find the correct answer.
If the only solution to the quadratic equation is 10, then the quadratic equation can be written as:
(x - 10)(x - 10) = 0
Expanding this equation, we get:
x^2 - 10x - 10x + 100 = 0
Simplifying further, we have:
x^2 - 20x + 100 = 0
So, the quadratic equation in standard form is:
x^2 - 20x + 100 = 0
To write a quadratic equation in standard form with the given solution, we need to use the factored form of a quadratic equation.
Given that the only solution is 10, we know that the equation can be written as (x - 10)(x - 10) = 0.
Expanding this equation, we get (x - 10)^2 = 0.
Next, we can expand the squared term to obtain (x - 10)(x - 10) = x^2 - 10x - 10x + 100 = x^2 - 20x + 100.
Therefore, the quadratic equation in standard form with the solution of 10 is x^2 - 20x + 100 = 0.