Algebra> Let P(x) =ax^2+bx+c, Q(x) =ax^2 +cx +b an...

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?

PRAMAY , 10 Years ago

Grade 11

1 Answers

Sourabh Singh

Last Activity: 10 Years ago

Find out theDiscriminantof all the equations by using the formula . After you have found out the determinant of the given quations you will find that Discriminant of R(x)is equal to the product ofP(x) andQ(x).
Discriminant of R(x) is negative. So product is negative , If one term is negative other has to be positive.
Option “B”