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BITSAT2016MathematicsDeterminantsActual

Let ₁, ₂ and ₁, ₂ be the roots of a x²+b x+c=0 and px ²+ qx + 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. Ab² q² = a c p r
  2. Bc ² r ² = ab pq
  3. Ca² p² = b c q r
  4. DNone of these

Correct answer

A. b² q² = a c p r

Step-by-step solution

Since ₁, ₂ and ₁, ₂ are the roots of ax ²+b x+c=0 and p x²+q x+r=0 respectively therefore ₁+ ₂= -b a , ₁ ₂= c a and ₁+ ₂= -q p , ₁ ₂= r p Since the given system of equation has a non-trivial solution | array ll ₁ & ₂ ₁ & ₂ array |=0 i.e. ₁ ₂- ₂ ₁=0 or ₁ ₁ = ₂ ₂ = ₁+ ₂ ₁+ ₂ = ₁ ₂ ₁ ₂ pb qa = pc ra b ² q ² = ac pr

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