If `a ,b ,c ,d in R ,` then the equation `(x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0` has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these

If a

If the equation ax^(2)+bx+c=x has no real roots,then the equation a(ax^(2)+bx+c)^(2)+b(ax^(2)+bx+c)+c=x will have a.four real roots b.no real root c.at least two least roots d.none of these

The equation (x/(x+1))^2+(x/(x-1))^2=a(a-1) has a. Four real roots if a >2 b.Four real roots if a<-1 c Two real roots if 1

If (x)=ax^(2)+bx+c amd Q(x)=-ax^(2)+dx+c,ac!=0P(x)=ax^(2)+bx+camdQ(x)=-ax^(2)+dx+c,ac!=0 then the equation P(x)*Q(x)=0 has a.exactly two real roots b.Atleast two real roots c.exactly four real roots d.no real roots

The quadratic equation 2x^(2)-sqrt5x+1=0 has (a) two distinct real roots (b) two equal real roots (c) no real roots (d) more than 2 real roots

If a,b,c in R and abc<0, then equation bcx^(2)+(2b+c-a)x+a=0 has (a).both positive roots (b) both negative roots (c).real roots (d) one positive and one negative root

If b_(1),b_(2)=2(c_(1)+c_(2),) then at least one of the equation x^(2)+b_(1)x+c_(1)=0andx^(2)+b_(2)x+c_(2)=0 has a.imaginary roots b.real roots c.purely imaginary roots d.none of these

For a , b , c non-zero, real distinct, the equation, (a^(2)+b^(2))x^(2)-2b(a+c)x+b^(2)+c^(2)=0 has non-zero real roots. One of these roots is also the root of the equation :

If (x)=ax^(2)+bx+c&Q(x)=-ax^(2)+dx+c,ac!=0P(x)=ax^(2)+bx+c&Q(x)=-ax^(2)+dx+c,ac!=0 then the equation P(x)*Q(x)=0 has (a) Exactly two real roots (b) Atleast two real roots (c)Exactly four real roots (d) No real roots