Find the value of a for the equation `x^2 + a |x| + 1 = 0` has (i) no roots (ii) two roots (iii) 3 roots (iv) 4 roots

Find the value of a if 1 is a root of the equation x^(2)+ax+3=0 .

(a^(2)-1)x^(2) + (a^(2) +5a+4)x+(a^(2) + 4a+3)=0 . Find the value of a for which (i) equation has two roots (ii) Equation has one real root (iii) It is an identity in x

Find the values of m for which the equation 3x^(2)+mx+2=0 has equal roots. Also, find the roots of the given equation.

For what integral values of a, the equation x^(2)-x(1-a)-(a+2)=0 has integral roots. Find the roots.

The equation x^(2) - 4x + 29 =0 has one root 2+ 5i. What is the other root?

Find the values of p for which the equation x^(4)-14x^(2)+24x-3-p=0 has (a) Two distinct negative real roots (b) Two real roots of opposite sign (c) Four distinct real roots (d) No real roots

Find the values of p for which the equation x^(4)-14x^(2)+24x-3-p=0 has (a) Two distinct negative real roots (b) Two real roots of opposite sign (c) Four distinct real roots (d) No real roots

Find the values of p for which the equation x^(4)-14x^(2)+24x-3-p=0 has (a) Two distinct negative real roots (b) Two real roots of opposite sign (c) Four distinct real roots (d) No real 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

Find value of k if equation x^(3)-3x^(2)+2=k has i 3 real roots ii) 1 real root