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Manipal MET2013MathematicsDeterminants

Let ₁, ₂ and ₁, ₂ be the roots of a x^2+b x+c=0 and p x^2+q x+r=0 respectively. If the system of equations ₁ y+ ₂ z=0 and ₁ y+ ₂ z=0 has a non-trivial solution, then

Options

  1. Ab^2 p r=q^2 a c
  2. Bb o r^2=q a c^2
  3. Cb p^2 r=q a^2 c
  4. DNone of these

Correct answer

A. b^2 p r=q^2 a c

Step-by-step solution

Given system has non-trivial solution then | array ll ₁ & ₂ ₁ & ₂ array |=0 ₁ ₂= ₂ ₁ array ll & ₁ ₁ = ₂ ₂ = ₁+ ₂ ₁+ ₂ = ₁ ₂ ₁ ₂ & -b / a -q / p = c / a r / p & b p a q = c p a r & b^2 p^2 a r=a^2 q^2 c p & b^2 p r=q^2 a c array

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