If the sum of the roots of the equation ax^2−2x+2a−0 is equal to their product, then the value of a is?

ax² − 2x + 2a = 0

We are told: Sum of roots = Product of roots

Step 1: Use formulas

For a quadratic equation ax² + bx + c = 0,

- Sum of roots = −b/a

- Product of roots = c/a

So here:

- Sum = −(−2)/a = 2/a

- Product = (2a)/a = 2

Set them equal:

2/a = 2

Multiply both sides by a:

2 = 2a

=> a = 1

Final Answer:

a = 1