If p, q, r are non-zero real numbers, the two equation, 2a2x2-2abx + b2 = 0 and p2x2+3pqx + q2 = 0 have :

Question

If p, q, r are non-zero real numbers, the two equation, 2a2x2-2abx + b2 = 0 and p2x2+3pqx + q2 = 0 have : (A) no common root (B) one common root if 2a2+b2 = p2 + q2 (C) two common roots if 3pq = 2ab (D) two common roots if 3qb = 2 ap

Tardigrade Admin · Accepted Answer

Discriminant of the equation 2a2x2-2abx + b2 = 0 is -4a2b2 < 0 and that of the equation p2x2+3pqx + q2 = 0 is 5p2q2 > 0 There cannot be any common root.

Q. If p, q, r are non-zero real numbers, the two equation, $2 a^{2} x^{2} - 2 ab x + b^{2} = 0$ and $p^{2} x^{2} + 3 pq x + q^{2} = 0$ have :

no common root

one common root if $2 a^{2} + b^{2} = p^{2} + q^{2}$

two common roots if $3 pq = 2 ab$

two common roots if $3 q b = 2 a p$

Discriminant of the equation
$2 a^{2} x^{2} - 2 ab x + b^{2} = 0$ is $- 4 a^{2} b^{2} < 0$ and that of the equation
$p^{2} x^{2} + 3 pq x + q^{2} = 0$ is $5 p^{2} q^{2} > 0$
There cannot be any common root.

Q. If p, q, r are non-zero real numbers, the two equation, 2a2x2−2abx+b2=0 and p2x2+3pqx+q2=0 have :

no common root

one common root if 2a2+b2=p2+q2

two common roots if 3pq=2ab

two common roots if 3qb=2ap

Discriminant of the equation 2a2x2−2abx+b2=0 is −4a2b2<0 and that of the equation p2x2+3pqx+q2=0 is 5p2q2>0 There cannot be any common root.

Q. If p, q, r are non-zero real numbers, the two equation, $2 a^{2} x^{2} - 2 ab x + b^{2} = 0$ and $p^{2} x^{2} + 3 pq x + q^{2} = 0$ have :

one common root if $2 a^{2} + b^{2} = p^{2} + q^{2}$

two common roots if $3 pq = 2 ab$

two common roots if $3 q b = 2 a p$

Discriminant of the equation
$2 a^{2} x^{2} - 2 ab x + b^{2} = 0$ is $- 4 a^{2} b^{2} < 0$ and that of the equation
$p^{2} x^{2} + 3 pq x + q^{2} = 0$ is $5 p^{2} q^{2} > 0$
There cannot be any common root.