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Let P(x) =ax^2+bx+c, Q(x) =ax^2 +cx +b and R(x) =ax^2+bcx+b^3+c^3-4abc where a,b,c belongs to R and a is not equal to zero. The equation R(x) =0 will have non real roots if (A) P(x) =0 has distinct real roots and Q(x)=0 has non-real roots. (B)P(x)=0 has non real roots and Q(x) =0 has distict real roots. (C)Both P(x) =0 and Q(x) =0 have non real roots.(D)Both P(x) =0 and Q(x) =0 have distict real roots. Which option is correct?

  1. Let P(x) =ax^2+bx+c, Q(x) =ax^2 +cx +b and R(x) =ax^2+bcx+b^3+c^3-4abc where a,b,c belongs to R and a is not equal to zero. The equation R(x) =0 will have non real roots if (A) P(x) =0 has distinct real roots and Q(x)=0 has non-real roots. (B)P(x)=0 has non real roots and Q(x) =0 has distict real roots.  (C)Both P(x) =0 and Q(x) =0 have non real roots.(D)Both P(x) =0 and Q(x) =0 have distict real roots. Which option is correct?
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Grade:11

1 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
6 years ago
Hi

Both option A & B are correct.
If you analyze Discriminent of R than you can wirte it in two factors which are (b^2-4ac)(c^2-4ab). So we have to analyze D of P & Q to get D of R<0 (desired condition)

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