The roots of the equation $$ax^2+x+b=0$$​ are equal if:

The quadratic equation:

​$$ax^2 + x + b = 0$$​​

For a quadratic equation $$ax^2 + bx + c = 0,$$​ the roots are equal if the discriminant is zero. The discriminant D for this equation is given by:

​$$D = b^2 – 4ac$$​​

From equation $$ax^2 + x + b = 0$$​, we have:

D = $$b^2 – 4ac = 1^2 - 4 \cdot a \cdot b$$​​

D = 1 − 4ab

For the roots to be equal, the discriminant must be zero:

D = 0

1−4ab = 0

4ab = 1

ab = $$\frac{1}{4}$$​​

Thus, ab = $$\bf\frac{1}{4}.$$​​