Question

For what positive values of ‘m’, roots of the following equations are equal, distinct and imaginary.

(1)

(2)

(3)

(4)

Answer 1

(1)

Comparing this equation with_,

Now,

(i) If the roots are equal, then

Hence, the positive value of m is.

(ii) If the roots are distinct, then

Hence,

(iii) If the roots are imaginary, then

Hence,

(2)

Comparing this equation with _,

Now,

(i) If the roots are equal, then

Hence, the positive value of m is.

(ii) If the roots are distinct, then

Hence,

(iii) If the roots are imaginary, then

Hence,

(3)

Comparing this equation with_,

Now,

(i) If the roots are equal, then

Hence, the positive value of m is .

(ii) If the roots are distinct, then

Hence,

(iii) If the roots are imaginary, then

Hence,

(4)

Comparing this equation with_,

Now,

(i) If the roots are equal, then

Hence, the positive value of m is.

(ii) If the roots are distinct, then

Hence,

(iii) If the roots are imaginary, then

Hence,