Explanation

A group generated by one of its elements is called a cyclic group.

This means that the group can be generated by repeatedly applying the group operation to a single element, called the generator.

In other words, all elements of the group can be expressed as powers of the generator.

Explanation

A monoid is a set with an associative binary operation and an identity element.

A group is a monoid where every element has an inverse.

Explanation

3x² - 7x - 6 = 0

We can factor the equation:

(3x + 2)(x - 3) = 0

This gives us two possible solutions:

3x + 2 = 0 --> 3x = -2 --> x = -2/3

x - 3 = 0 --> x = 3

So, the roots of the equation are x = -2/3 and x = 3.

The correct answer is:

3, -2/3

Explanation

The quadratic equation whose roots are reciprocal of:

2x2 + 5x + 3 = 0 can be obtained by replacing x by 1/x.

Hence, 2(1/x)2 + 5(1/x) + 3 = 0

=> 3x^2 + 5x + 2 = 0

Explanation

Let the two consecutive positive integers be x and x + 1

x2 + (x + 1)2 - x(x + 1) = 91

x2 + x - 90 = 0

(x + 10)(x - 9) = 0 => x = -10 or 9.

As x is positive x = 9

Hence the two consecutive positive integers are 9 and 10.