If one of the roots of the equation x2+ax-b=0 is 1, then what is the value of (a-b)

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  1. -1 
  2. -2
  3. 2
  4. 1

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Option 1 : -1 
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 Given: The quadratic equation is: x2 + ax - b = 0

One of the roots of this equation is 1.

Concept Used:

For a quadratic equation: x2 + px + q = 0 If r is a root, it satisfies the equation: r2 + pr + q = 0

Substituting r = 1 in the given equation: 12 + a(1) - b = 0

Calculation:

Step 1: Substitute r = 1 into x2 + ax - b = 0.   ⇒ 12 + a(1) - b = 0  

Step 2: Simplify the equation.   ⇒ 1 + a - b = 0  

Step 3: Rearrange to find a - b.  

⇒ a - b = -1 Conclusion:  

∴ The value of (a - b) is -1.

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