Advanced Mathematics help ASAP?

Question

sin(ax-x^2)=0 .. sum of all solutions of this function is 100 , what is "a" equal to ?

Answer 1

The equation is sin(ax - x²) = 0.

sin(ax - x²) = sin(0)

The genaral solution of sin(θ) = sin(α) is θ = nπ + (-1)ⁿα, where n is an integer.

So, ax - x² = nπ + (-1)ⁿ(0)

ax - x² = nπ

ax - x² - nπ = 0

x² - ax + nπ = 0.

If α and β are the two root of the quadratic equation is ax² + bx + c = 0, then,

Sum of the roots(α + β) = - coefficient of x/coefficient of x²

x² - ax + nπ = 0, is a quadratic equation.

So, sum of the root(α + β) = - (- a)/1.

100 = a            (From the given data)

⇒ a = 100.

The value of a = 100.