write a quadratic equation in the variable x having the given numbers as solution. Type the equation in standard form, ax^2+bx+c=0
solution 4, only solution
You left out the numbers
assume p and q
then
(x-p)(x-q) = 0
multiply it out
no numbers left out
So what were the given numbers?
Oh, you mean the number 4 is the solution? Then 4 and 4
(x-4)(x-4) = 0
x^2 - 8 x + 16 = 0
To find a quadratic equation with a solution of 4, we can use the fact that if one value is a solution, then its conjugate is also a solution. Since we only have one solution, the other solution is also 4.
To write the quadratic equation in standard form, we use the fact that if a and b are the solutions of a quadratic equation, then the equation can be written as (x - a)(x - b) = 0.
In this case, the equation becomes:
(x - 4)(x - 4) = 0
Expanding this equation, we get:
x^2 - 8x + 16 = 0
So, the quadratic equation with the solution 4 is:
x^2 - 8x + 16 = 0, which is in standard form (ax^2 + bx + c = 0) with a = 1, b = -8, and c = 16.