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KVPY2012MathematicsQuadratic Equation

Suppose a , b , c are real numbers, and each of the equations x ²+2 ax + b ²=0 and x ²+2 bx + c ²=0 has two distinct real roots. Then the equation x ²+2 cx + a ²=0 has-

Options

  1. ATwo distinct positive real roots
  2. BTwo equal roots
  3. COne positive and one negative root
  4. DNo real roots

Correct answer

D. No real roots

Step-by-step solution

x ²+2 ax + b ²=0 x ²+2 bx + c ²=0 array ll D₁>0 & D₂>0 4 a²+b²>0 & 4 b²-4 c²>0 a²>b² .(1) & b²>c² . .(2) array From (1) and (2)a²>b²>c² a²>c² c²-a² < 0x²+2 c x+a²=0D=4 c²-4 a² < 0 No real roots

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