If λ ∈ R such that the origin and the non-real roots of the equation 2z2+2z+λ =0 form the vertices of an equilateral triangle in the argand plane, then (1/λ ) is equal to

Question

If λ ∈ R such that the origin and the non-real roots of the equation 2z2+2z+λ =0 form the vertices of an equilateral triangle in the argand plane, then (1/λ ) is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Let, z1 and z2 are roots of the equation 2z2+2z+λ =0 ⇒ z1+z2=-1andz1z2=(λ /2) If 0,z1 &z2 form an equilateral triangle, then z12+z22=z1z2 ⇒ (z1 + z2)2=3z1z2 ⇒ (- 1)2=3((λ /2))⇒ (1/λ )=(3/2)=1.5

Q. If λ∈R such that the origin and the non-real roots of the equation 2z2+2z+λ=0 form the vertices of an equilateral triangle in the argand plane, then λ1​ is equal to

Let, z1​ and z2​ are roots of the equation 2z2+2z+λ=0 ⇒z1​+z2​=−1andz1​z2​=2λ​ If 0,z1​&z2​ form an equilateral triangle, then z12​+z22​=z1​z2​ ⇒(z1​+z2​)2=3z1​z2​ ⇒(−1)2=3(2λ​)⇒λ1​=23​=1.5

Q. If $λ \in R$ such that the origin and the non-real roots of the equation $2 z^{2} + 2 z + λ = 0$ form the vertices of an equilateral triangle in the argand plane, then $\frac{1}{λ}$ is equal to