Chapter 12

Solve by quadratic formula. Give your answers in decimal form to three significant digits. Check some by calculator. $$x^{2}+5 x-6=0$$

What fraction added to its reciprocal gives \(2 \frac{1}{6} ?\)

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Explicit Functions. $$x^{2}-12 x+28=0$$

Solve by quadratic formula. Give your answers in decimal form to three significant digits. Check some by calculator. $$x^{2}-22 x+8=0$$

Find three consecutive numbers such that the sum of their squares will be 434

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Explicit Functions. $$x^{2}-6 x+7=0$$

Solve by quadratic formula. Give your answers in decimal form to three significant digits. Check some by calculator. $$x^{2}-12 x+3=0$$

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Explicit Functions. $$x^{2}+x-19=0$$

Solve by quadratic formula. Give your answers in decimal form to three significant digits. Check some by calculator. $$x^{2}+2 x-7=0$$

Find two numbers whose sum is 11 and whose product is \(30 .\)

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Explicit Functions. $$x^{2}-x-13=0$$

Solve by quadratic formula. Give your answers in decimal form to three significant digits. Check some by calculator. $$2 x^{2}-15 x+9=0$$

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Explicit Functions. $$3 x^{2}+12 x-35=0$$

Solve by quadratic formula. Give your answers in decimal form to three significant digits. Check some by calculator. $$3 x^{2}-10 x+6=0$$

A number increased by its square is equal to 9 times the next higher number. Find the number.

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Explicit Functions. $$29.4 x^{2}-48.2 x-17.4=0$$

Solve by quadratic formula. Give your answers in decimal form to three significant digits. Check some by calculator. $$5 x^{2}-25 x+4=0$$

A rectangle is to be 2 m longer than it is wide and have an area of \(24 \mathrm{m}^{2}\). Find its dimensions.

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Explicit Functions. $$36 x^{2}+3 x-7=0$$

Solve by quadratic formula. Give your answers in decimal form to three significant digits. Check some by calculator. $$5 x^{2}+22 x+3=0$$

One leg of a right triangle is \(3 \mathrm{cm}\) greater than the other leg, and the hypotenuse is \(15 \mathrm{cm} .\) Find the legs of the triangle.

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Explicit Functions. $$28 x^{2}+29 x+7=0$$

Challenge Problems $$1.22 x^{2}-11.5 x+9.89=0$$

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Explicit Functions. $$49 x^{2}+21 x-5=0$$

Challenge Problems $$5.11 x^{2}+18.6 x+3.88=0$$

The length, width, and height of a cubical shipping container are all decreased by \(1.0 \mathrm{ft},\) thereby decreasing the volume of the cube by \(37 \mathrm{ft}^{3} .\) What was the volume of the original container?

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Explicit Functions. $$16 x^{2}-16 x+1=0$$

Challenge Problems $$2.96 x^{2}-33.2 x+4.05=0$$

Find the dimensions of a rectangular field that has a perimeter of 724 m and an area of \(32,400 \mathrm{m}^{2}\)

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Explicit Functions. $$3 x^{2}-10 x+4=0$$

Challenge Problems $$3.22 x^{2}+9.66 x+2.85=0$$

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Explicit Functions. $$x^{2}-34 x+22=0$$

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Implicit Functions. $$3 x^{2}+5 x=7$$

Challenge Problems $$3 x^{2}=17 x-6$$

Challenge Problems $$3.25-31.0 x^{2}=4.99 x-63.5$$

A truck travels 350 mi to a delivery point, unloads, and, now empty, returns to the starting point at a speed 8.00 milh greater than on the outward trip. What was the speed of the outward trip if the total round-trip driving time was \(14.4 \mathrm{h} ?\)

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Implicit Functions. $$x^{2}-6 x-14=3$$

Challenge Problems $$3.88\left(x^{2}+7.72\right)=6.34 x(3.99 x-3.81)+7.33$$

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Implicit Functions. $$6 x-300=205-3 x^{2}$$

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Implicit Functions. $$3 x^{2}-25 x=5 x-73$$

In the quadratic formula, the quantity under the radical sign, \(b^{2}-4 a c,\) is called the discriminant. It can be used to predict whether the roots are real and equal, real and unequal, or not real. Try different values of \(a, b\) and \(c\) to give different values for the discriminant. See if you can arrive at some rules for predicting roots, based on the value of the discriminant.

A boat sails \(30 \mathrm{km}\) at a uniform rate. If the rate had been \(1 \mathrm{km} / \mathrm{h}\) more, the time of the sailing would have been 1 h less. Find the rate of travel.

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Implicit Functions. $$2 x^{2}+100=32 x-11$$

A certain punch press requires 3 h longer to stamp a box of parts than does a newer-model punch press. After the older press has been punching a box of parts for \(5 \mathrm{h}\), it is joined by the newer machine. Together, they finish the box of parts in 3 additional hours. How long does it take each machine, working alone, to punch a box of parts?

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Implicit Functions. $$33-3 x^{2}=10 x$$

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Challenge Problems. $$1.83 x^{2}-4.26=4.82 x+7.28$$

A woman worked part-time a certain number of days, receiving for her pay \(\$ 1800 .\) If she had received \(\$ 10\) per day less than she did, she would have had to work 3 days longer to earn the same sum. How many days did she work?

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Challenge Problems. $$6.47 x-338=205-3.73 x^{2}$$

Find the roots of each quadratic by any of the methods shown in this section. Keep three significant digits. For some, use more than one method and compare results. Challenge Problems. $$x(2 x-3)=3 x(x+4)-2$$

Use \(s=v_{0} t+\frac{1}{2} g t^{2}\) for these falling-body problems, but be careful of the signs. If you take the upward direction as positive, \(g\) will be negative. An object is thrown upward with a velocity of \(145 \mathrm{ft} / \mathrm{s}\). When will it be \(85.0 \mathrm{ft}\) above its initial position? \(\left(g=32.2 \mathrm{ft} / \mathrm{s}^{2}\right)\)