Chapter A.7, Problem 3AYU

To determine

To find: Whether the statement is true or false.

Answer to Problem 3AYU

The statement is false.

Explanation of Solution

Given information:

The given statement is “In athe complex number system, a quadratic equation has four siolution”.

Calculation:

In general a quadratic equation has two roots and their nature depends on the discriminant.

A quadratic equation always has only two roots weather the roots are real or complex.

Foer the complex roots the value of discriminant should be less than zero.

Assume a quadratic equation.

$a{x}^2+bx+c=0$

The discriminate will be $b^2-4ac$ .

If $b^2-4ac<0$ the roots will be complex but the roots will still be $2$ in number. The complex roots are always conjugae

Therefore, the given statement false.