write a quadratic equation in the variable x having the given numbers as solutions. Use ax^2 + bx + c=0
Thanks so much for the help
I forgot to give the given numbers. -sqrt10 and 8sqrt10
x = -sqrt(10), x = 8sqrt(10).
x + sqrt(10) = 0,
x - 8sqrt(10) = 0,
(x + sqrt(10) (x - 8sqrt(10) = 0,
x^2 - 8sqrt(10)x + sqrt(10)x - 80 = 0,
Eq: x^2 - 7sqrt(10)x - 80 = 0.
To write a quadratic equation in the form ax^2 + bx + c = 0, we need to know the solutions first. Let's assume the two solutions are "p" and "q". From this information, we can write two equations:
1. (x - p) = 0
2. (x - q) = 0
To find the quadratic equation, we need to multiply these two equations together. So, multiplying equation 1 by equation 2, we get:
(x - p)(x - q) = 0
Expanding the equation, we have:
x^2 - qx - px + pq = 0
Simplifying further, we get:
x^2 - (p + q)x + pq = 0
Now we can substitute "a", "b", and "c" into the equation. Therefore, the quadratic equation with the given solutions p and q is:
ax^2 + bx + c = 0, where a = 1, b = -(p + q), and c = pq.