Chapter 4.6, Problem 11CYU

(a)

To determine

To evaluate:

The value of the given number.

Answer to Problem 11CYU

The value of given operation is $\frac{-3-3i}{2},\frac{-3+3i}{2}$ .

Explanation of Solution

Given:

The order of operation

  $2x^2-6x+9=0$

Concept used:

Product means the answer to a multiplication problem.

Sum means the total amount resulting from the addition of two or more numbers amounts or items.

Quotient means a result obtained by dividing one quantity by another.

Calculation:

The order of operation

  $\begin{array}{l}2x^2-6x+9=0\\ =\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-6\pm \sqrt{6^2-4\left(9\right)\left(2\right)}}{2\left(2\right)}\\ =\frac{-6\pm \sqrt{36-72}}{4}\\ =\frac{-6\pm \sqrt{-36}}{4}\\ =\frac{\left(-6\pm 6i\right)}{4}\\ =\frac{-3-3i}{2},\frac{-3+3i}{2}\end{array}$

Therefore,

The value of given operation is $\frac{-3-3i}{2},\frac{-3+3i}{2}$ .

(b)

To determine

To evaluate:

The value of the given number.

Answer to Problem 11CYU

The value of given operation is complex roots.

Explanation of Solution

Given:

The order of operation

  $2x^2-6x+9=0$

Concept used:

Product means the answer to a multiplication problem.

Sum means the total amount resulting from the addition of two or more numbers amounts or items.

Quotient means a result obtained by dividing one quantity by another.

Calculation:

The order of operation

  $\begin{array}{l}2x^2-6x+9=0\\ =\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-6\pm \sqrt{6^2-4\left(9\right)\left(2\right)}}{2\left(2\right)}\\ =\frac{-6\pm \sqrt{36-72}}{4}\\ =\frac{-6\pm \sqrt{-36}}{4}\\ =\frac{\left(-6\pm 6i\right)}{4}\\ =\frac{-3-3i}{2},\frac{-3+3i}{2}\end{array}$

Therefore,

The value of given operation is complex roots.