If the roots of the equation `x^(2)-4x-log_3 a=0` , are real , the least value of a is :

If the roots of the quadratic equation x^(2)-4x-log_(3)a=0 are real,then the least value of a is

If the roots of the equation x^(2) - 4x- log_(3) N =0 are real, then what is the minimum vlaue of N?

the real roots of the equation |x^(2)+4x+3|+2x+5=0 are

If the roots of the quadratic equation x^(2) - 4x- log_(10) N= 0 are all real, then the minimum value of N is

The real roots of the equation |x^2 +4x +3|+2x +5 =0 are

If the roots of the equation x^2+x+a=0 be real and unequal, then prove that the roots of the equation 2x^2-4(1+a)x+2a^2+3=0 are imaginary (a is real).

For what values of k ,the roots of the equation x^(2)+4x+k=0 are real?