# If The Roots of The Equation x² – nx + m = 0 Differ by 1 :

If the roots of the equation x² – *nx* +* m* = 0 differ by 1, then

*n*4^{2}–*m*– 1=0*n*^{2}+ 4*m*– 1=0*m*^{2}+ 4*n*+1=0*m*^{2}– 4*n*-1=0

**Answer: (1) n ^{2} – 4 m – 1 = 0
**

**Explanation:-**

α + β = n and αβ = m

Then, (α – β)² = 1

And (α + β)² – 4 αβ = 1

Put the value of α + β = n and αβ = m

Then, n² – 4 m = 1

n² – 4 m – 1 = 0

If the roots of the equation x² – nx + m = 0 Differ by 1 then, n² – 4 m – 1 = 0

Hence, the answer is (1) n² – 4 m – 1 = 0