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
- n2 – 4m – 1=0
- n2 + 4m – 1=0
- m2 + 4n +1=0
- m2 – 4n-1=0
Answer: (1) n2 – 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