The origin and the roots of the equation z 2+ pz + q =0 form an equilateral triangle if -

Question

The origin and the roots of the equation z 2+ pz + q =0 form an equilateral triangle if - (A) p 2=2 q (B) p 2= q (C) p2=3 q (D) q2=3 p

Tardigrade Admin · Accepted Answer

z2+p z+q=0 z1+z2=-p, z1 z2=q If z1, z2, z3 are the vertices of an equilateral triangle then z12+z22+z32=z1 z2+z2 z3+z3 z1 If z3 is origin then z12+z22=z1 z2 ⇒(z1+z2)2=3 z1 z2 ⇒ p2=3 q

Q. The origin and the roots of the equation $z^{2} + p z + q = 0$ form an equilateral triangle if -

$p^{2} = 2 q$

$p^{2} = q$

$p^{2} = 3 q$

$q^{2} = 3 p$

Q. The origin and the roots of the equation z2+pz+q=0 form an equilateral triangle if -

p2=2q

p2=q

p2=3q

q2=3p

z2+pz+q=0 z1​+z2​=−p,z1​z2​=q If z1​,z2​,z3​ are the vertices of an equilateral triangle then z12​+z22​+z32​=z1​z2​+z2​z3​+z3​z1​ If z3​ is origin then z12​+z22​=z1​z2​ ⇒(z1​+z2​)2=3z1​z2​⇒p2=3q

Q. The origin and the roots of the equation $z^{2} + p z + q = 0$ form an equilateral triangle if -

$p^{2} = 2 q$

$p^{2} = q$

$p^{2} = 3 q$

$q^{2} = 3 p$