Let α 1,α 2 and β 1,β 2 are roots of the equation ax2+bx+c=0 and px2+qx+r=0 respectively. If the system of equations α 1y+α 2z=0 and β 1y+β 2z=0 has a non trivial solution, then

Question

Let α 1,α 2 and β 1,β 2 are roots of the equation ax2+bx+c=0 and px2+qx+r=0 respectively. If the system of equations α 1y+α 2z=0 and β 1y+β 2z=0 has a non trivial solution, then (A) bpr 2=qac2 (B) b2pr=q2ac (C) bp2r=qa2c (D) none of these

Tardigrade Admin · Accepted Answer

| α 1 α 2 β 1 β 2 |=0⇒ α 1β 2-α 2β 1=0⇒ (α 1/α 2)=(β 1/β 2) Using componendo and dividendo (α 1 + α 2/α 1 - α 2)=(β 1 + β 2/β 1 - β 2)⇒ (- b / a/√(b2)a2 - (4 c)a=(- q / p/√(q2)p2 - (4 r)p ⇒ (b/√b2 - 4 a c)=(q/√q2 - 4 p r)⇒ b/2)pr=q/2)ac

Q. Let $α_{1}, α_{2}$ and $β_{1}, β_{2}$ are roots of the equation $a x^{2} + b x + c = 0$ and $p x^{2} + q x + r = 0$ respectively. If the system of equations $α_{1} y + α_{2} z = 0$ and $β_{1} y + β_{2} z = 0$ has a non trivial solution, then

$b p r$ $_^{2} = q a c^{2}$

$b^{2} p r = q^{2} a c$

$b p^{2} r = q a^{2} c$

none of these

Q. Let α1​,α2​ and β1​,β2​ are roots of the equation ax2+bx+c=0 and px2+qx+r=0 respectively. If the system of equations α1​y+α2​z=0 and β1​y+β2​z=0 has a non trivial solution, then

bpr _2=qac2

b2pr=q2ac

bp2r=qa2c

none of these

Q. Let $α_{1}, α_{2}$ and $β_{1}, β_{2}$ are roots of the equation $a x^{2} + b x + c = 0$ and $p x^{2} + q x + r = 0$ respectively. If the system of equations $α_{1} y + α_{2} z = 0$ and $β_{1} y + β_{2} z = 0$ has a non trivial solution, then

$b p r$ $_^{2} = q a c^{2}$

$b^{2} p r = q^{2} a c$

$b p^{2} r = q a^{2} c$