CBSE Class 10 Answered
The equation x2 + λx + (λ + 1.25) = 0 has coincident roots.
means the discriminant is zero, i.e D = 0.
D = b2 - 4ac = 0
λ2 - 4 × 1 × (λ + 1.25) = 0
λ2 - 4λ - 5 = 0
λ2 - 5λ + λ - 5 = 0
λ (λ - 5) + 1(λ - 5) = 0
(λ - 5) (λ + 1) = 0
(λ - 5) = 0 or (λ +1) = 0
λ = 5 or λ = -1
Therefore , for λ = 5 or -1 , the roots of the given Quadratic Equation are Coincident.
The equation x2 + λx + (λ + 1.25) = 0 has distinct roots.
means the discriminant is not equal to zero, i.e D ≠ 0.
We already know that for λ = 5 or -1 , the roots of the given Quadratic Equation are Coincident means D = 0.
Therefore except λ = 5 or -1 , the value of D is non- zero.
Therefore for all the real values of λ except 5 and -1, the roots of the given Quadratic Equation are Coincident.