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 the equation a x^2+b x+c=x has no real roots, then the equation a(a x^2+b x+c)^2+b(a x^2+b x+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 2 d. none of these

If 3(a+2c)=4(b+3d), then the equation a x^3+b x^2+c x+d=0 will have (a)no real solution (b)at least one real root in (-1,0) (c)at least one real root in (0,1) (d)none of these

Prove that the equation x^(2)(a^(2)b^(2))+2x(ac+bd)+(c^(2)+d^(2))=0 has no real root if adnebc .

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 a ,b ,c in Ra n da b c<0 , then equation b c x^2+2(b+c-a)x+a=0h a s (a)both positive roots (b)both negative roots (c)real roots (d)one positive and one negative root

Let a >0,b >0 and c >0 . Then, both the roots of the equation a x^2+b x+c=0 are a. real and negative b.have negative real parts c. have positive real parts d. None of the above

If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has atleast one real root between 0 to 1.

If a ,b ,c in R , then find the number of real roots of the equation =|x c-b-c x a b-a x|=0

If he equation x^3+a x^2+b x+216=0 has three real roots in G.P., then b//a has the value equal to _____.