Chapter 4.6, Problem 35PPS

(a)

To determine

To evaluate:

The value of the given number.

Answer to Problem 35PPS

The value of given operation is $-\frac{8}{5},0$ .

Explanation of Solution

Given:

The order of operation

  $5x^2+8x=0$

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

  $\begin{array}{l}5x^2+8x=0\\ =\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-8\pm \sqrt{8^2-4\left(5\right)\left(0\right)}}{2\left(5\right)}\\ =\frac{-8\pm \sqrt{8^2}}{10}\\ =\frac{-8\pm 8}{10}\\ =\frac{-8-8}{10},\frac{-8+8}{10}\\ =-\frac{8}{5},0\end{array}$

Therefore,

The value of given operation is $-\frac{8}{5},0$

(b)

To determine

To evaluate:

The value of the given number.

Answer to Problem 35PPS

The value of given operation is real roots.

Explanation of Solution

Given:

The order of operation

  $2x^2+3x-3=0$

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

  $\begin{array}{l}5x^2+8x=0\\ =\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-8\pm \sqrt{8^2-4\left(5\right)\left(0\right)}}{2\left(5\right)}\\ =\frac{-8\pm \sqrt{8^2}}{10}\\ =\frac{-8\pm 8}{10}\\ =\frac{-8-8}{10},\frac{-8+8}{10}\\ =-\frac{8}{5},0\end{array}$

Therefore,

The value of given operation is real roots.

(c)

To determine

To evaluate:

The exact value of the given number.

Answer to Problem 35PPS

The exact value of given operation is $-1.6,0$ .

Explanation of Solution

Given:

The order of operation

  $2x^2+3x-3=0$

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

  $\begin{array}{l}5x^2+8x=0\\ =\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-8\pm \sqrt{8^2-4\left(5\right)\left(0\right)}}{2\left(5\right)}\\ =\frac{-8\pm \sqrt{8^2}}{10}\\ =\frac{-8\pm 8}{10}\\ =\frac{-8-8}{10},\frac{-8+8}{10}\\ =-\frac{8}{5},0\\ =-1.6,0\end{array}$

Therefore,

The value of given operation is $-1.6,0$