Question

Determine the nature of the roots of the following equations.

(1)

(2)

(3)

(4)

(5)

(6)

Answer 1

(1)

Comparing this equation with_,

Let

Hence, the roots are real, irrational and distinct.

(2)

Comparing this equation with_,

Let

Hence, the roots are imaginary.

(3)

Comparing this equation with_,

Let

Hence, the roots are real, irrational and distinct.

(4)

Comparing this equation with_,

Let

Hence, the roots are real, rational and equal.

(5)

Comparing this equation with_,

Let

Hence, the roots are real, rational and distinct.

(6)

Comparing this equation with_,

Let

Hence, the roots are imaginary.