Chapter 4.6, Problem 39PPS

(a)

To determine

To evaluate:

The value of the given number.

Answer to Problem 39PPS

The value of given operation is $\frac{-1.4\pm \sqrt{13.48}}{1.2}$ .

Explanation of Solution

Given:

The order of operation

  $0.6x^2+1.4x-4.8=0$

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

  $\begin{array}{l}0.6x^2+1.4x-4.8=0\\ =\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-1.4\pm \sqrt{{1.4}^2-4\left(0.6\right)\left(-4.8\right)}}{2\left(0.6\right)}\\ =\frac{-1.4\pm \sqrt{1.96+11.52}}{1.2}\\ =\frac{-1.4\pm \sqrt{13.48}}{1.2}\\ =\frac{-1.4-\sqrt{13.48}}{1.2},\frac{-1.4+\sqrt{13.48}}{1.2}\end{array}$

Therefore,

The value of given operation is $\frac{-1.4\pm \sqrt{13.48}}{1.2}$

(b)

To determine

To evaluate:

The value of the given number.

Answer to Problem 39PPS

The value of given operation is real roots.

Explanation of Solution

Given:

The order of operation

  $0.6x^2+1.4x-4.8=0$

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

  $\begin{array}{l}0.6x^2+1.4x-4.8=0\\ =\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-1.4\pm \sqrt{{1.4}^2-4\left(0.6\right)\left(-4.8\right)}}{2\left(0.6\right)}\\ =\frac{-1.4\pm \sqrt{1.96+11.52}}{1.2}\\ =\frac{-1.4\pm \sqrt{13.48}}{1.2}\\ =\frac{-1.4-\sqrt{13.48}}{1.2},\frac{-1.4+\sqrt{13.48}}{1.2}\end{array}$

Therefore,

The value of given operation is real roots.

(c)

To determine

To evaluate:

The exact value of the given number.

Answer to Problem 39PPS

The exact value of given operation is $-4.4,1.6$ .

Explanation of Solution

Given:

The order of operation

  $0.6x^2+1.4x-4.8=0$

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

  $\begin{array}{l}0.6x^2+1.4x-4.8=0\\ =\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-1.4\pm \sqrt{{1.4}^2-4\left(0.6\right)\left(-4.8\right)}}{2\left(0.6\right)}\\ =\frac{-1.4\pm \sqrt{1.96+11.52}}{1.2}\\ =\frac{-1.4\pm \sqrt{13.48}}{1.2}\\ =\frac{-1.4-\sqrt{13.48}}{1.2},\frac{-1.4+\sqrt{13.48}}{1.2}\\ =\frac{-1.4-3.6}{1.2},\frac{-1.4+3.6}{1.2}\\ =-4.4,1.6\end{array}$

Therefore,

The value of given operation is $-4.4,1.6$