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?
Answer: 1
Explanation
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
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