Equation `(x)2)(x+3)(x+8)(x+12)=4x^2` has four real and distinct roots two irrational roots two integer roots two imaginary roots

Equation 12x^(4)-56x^(3)+89x^(2)-56x+12=0 has four real and distinct roots two irrational roots one integer root two imaginary roots

The equation x^(5)+x^(4)+1=0 has (1) One real and four imaginary roots (2) Five real roots (3) Three real and two imaginary roots (4) Three real roots in which two are same and two imaginary roots

(x^(2)+1)^(2)-x^(2)=0 has (i) four real roots (ii) two real roots (iii) no real roots (iv) one real root

If p and q are odd integers, then the equation x^2+2px+2q=0 (A) has no integral root (B) has no rational root (C) has no irrational root (D) has no imaginary root

If p and q are odd integers, then the equation x^2+2px+2q=0 (A) has no integral root (B) has no rational root (C) has no irrational root (D) has no imaginary root

The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has only purely imaginary roots at real roots two real and purely imaginary roots neither real nor purely imaginary roots

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 c. Two real roots if 1 d . No real roots if a<-1

Let a ,b ,cR_0 and each of the quadratic equations in x ,x^2+2(a^2+b^2)x+(b^2+c^2)^2=0 and x^2+2(b^2+c^2)x+(c^2+a^2)^2=0 has two distinct real roots. Then equation x^2+2(c^2+a^2)x+(a^2+b^2)^2=0 ha Two distinct positive real roots Two equal real roots Two distinct negative real roots (4) No real roots

If a, b , c in R and 3b^(2)-8ac lt 0 , then the equation ax^(4)+bx^(3)+cx^(2)+5x-7=0 has a) all real roots b) all imaginary roots c)exactly two real and two imaginary roots d) none

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