Write an equation that has the given solutions. 0, 2, and 9
x(x-2)(x-9) = 0
Sure! Here's an equation that has the given solutions: (x - 0)(x - 2)(x - 9) = 0. Now, be careful not to trip over those solutions!
To write an equation with the given solutions of 0, 2, and 9, we can start by using the fact that the solutions are the values that make the equation equal to zero.
Let's assume the equation is in the form of a quadratic equation: ax^2 + bx + c = 0.
Now, we can substitute the solutions into the equation and solve for the values of a, b, and c.
First, let's substitute x = 0:
a(0)^2 + b(0) + c = 0
0 + 0 + c = 0
c = 0
Second, let's substitute x = 2:
a(2)^2 + b(2) + c = 0
4a + 2b + c = 0
Lastly, let's substitute x = 9:
a(9)^2 + b(9) + c = 0
81a + 9b + c = 0
Now, we can summarize the coefficients by representing them in a matrix:
[4, 2, 1; 81, 9, 1]
To find the equation from this matrix, we can expand the determinant of it:
(4(9) - 81(2))x + (81(1) - 4(1))y + (2(2) - 4(81))z = 0
Simplifying further:
-162x -3y - 320z = 0
Therefore, the equation with the given solutions of 0, 2, and 9 is:
-162x -3y - 320z = 0
To write an equation with the given solutions of 0, 2, and 9, we can use the fact that a polynomial equation has solutions that correspond to its zeros.
Let's assume the equation is in standard form:
(x - r1)(x - r2)(x - r3) = 0,
where r1, r2, and r3 are the given solutions.
Substituting the values 0, 2, and 9 into the equation, we have:
(x - 0)(x - 2)(x - 9) = 0.
Multiplying this out gives us:
x(x - 2)(x - 9) = 0.
This is our equation with the given solutions of 0, 2, and 9.