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

(i) Find the value of k for which x=1 is a root of the equation x^(2)+kx+3=0. Also, find the other root. (ii) Find the values of a and b for which x=(3)/(4)" and "x=-2 are the roots of the equation ax^(2)+bx-6=0.

Fomd the value of a when (-1) is a root of the equation x^2 + ax + 3= 0

Find the set of all values of a for which the roots of the equation x^(2)-2ax+a^(2)+a-3=0 are less than 3

If the absolute value of the difference of the roots of the equation x^(2) + ax + 1 = 0 "exceeds" sqrt(3a) , then

If the absolute value of the difference of the roots of the equation x^(2) + ax + 1 = 0 "exceeds" sqrt(3a) , then

Find the set of all values of a for which the roots of the equation x^2-2ax + a^2 + a-3=0 are less than 3,

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 all values of 'a' for which exactly one root of equation x^(2)+3ax+a+1=0 lies in (0, 1) or (3,4)