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 a>2 d. none of these

The equation ax^(4)-2x^(2)-(a-1)=0 will have real and unequal roots if

The equation x-2/(x-1)=1-2/(x-1) has a. no root b. one root c. two equals roots d. Infinitely many roots

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-2//x-1=1-2//x-1 has a. no root b. one root c. two equals roots d. Infinitely many roots

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

If the equation x^4- λx^2+9=0 has four real and distinct roots, then lamda lies in the interval

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

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 _____.

x ^(2) +1 has no real zeroes. Why ?