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Determine λ so that the equation x2 + λx  + λ + 1.25 = 0 has Two distinct roots Two coincident roots.

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.

Answered by Yasmeen Khan | 24 Sep, 2018, 01:12: PM

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