Question

Solve this quadratic function 1+10q-2q²=0

Answer 1

To solve the quadratic function 1+10q-2q²=0, we will first rewrite the equation in the standard form of a quadratic function, which is ax^2 + bx + c = 0.

The given equation is:
1 + 10q - 2q^2 = 0

Rearranging it in the standard form:
-2q^2 + 10q + 1 = 0

Now, we can solve this quadratic equation using the quadratic formula:
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a

For the given equation:
a = -2, b = 10, c = 1

Plug these values into the quadratic formula:
q = (-10 ± √(10^2 - 4(-2)(1))) / 2(-2)
q = (-10 ± √(100 + 8)) / -4
q = (-10 ± √108) / -4
q = (-10 ± 10.39) / -4

Now, we have two possible solutions for q:
q = (-10 + 10.39) / -4 = 0.0975
q = (-10 - 10.39) / -4 = 5.0975

Therefore, the solutions for the quadratic function 1+10q-2q²=0 are q = 0.0975 and q = 5.0975.