Chapter Questions
If $a b=0$, what is known about either $a$ or $b$ ?
Solve for $x: 3 x(x-2)=0$
Solve each equation by factoring:$x^2-4=0$
Solve each equation by factoring:$x^2-x=6$
Solve each equation by factoring:$5 x^2-6 x=0$
Solve each equation by factoring:$x^2-3 x-28=0$
Solve each equation by factoring: $x^2-14 x=-45$
Solve each equation by factoring:$x^2-18-3 x=0$
Solve each equation by factoring:$3 x^2+20 x+32=0$
Solve each equation using the quadratic formula (when necessary, round results to three significant digits):$3 x^2-16 x-12=0$
Solve each equation using the quadratic formula (when necessary, round results to three significant digits):$x^2+7 x-5=0$
Solve each equation using the quadratic formula (when necessary, round results to three significant digits):$2 x^2+x=15$
Solve each equation using the quadratic formula (when necessary, round results to three significant digits): $x^2-4 x=2$
Solve each equation using the quadratic formula (when necessary, round results to three significant digits):$3 x^2-4 x=5$
The area of a piece of plywood is $36 \mathrm{ft}^2$. Its length is $5 \mathrm{ft}$ more than its width. Find its length and width.
A variable electric current is given by the formula $i=t^2-12 t+36$, where $t$ is in $\mu \mathrm{s}$. At what times is the current $i$ equal to a. $4 \mathrm{~A}$ ? b. $0 \mathrm{~A}$ ? c. $10 \mathrm{~A}$ ?
Draw the graph of each equation and label each vertex:$y=x^2-x-6$
Draw the graph of each equation and label each vertex:$y=-3 x^2+2$
Express each number in terms of $j$ : $\sqrt{-36}$
Express each number in terms of $j$ : $\sqrt{-73}$
Simplify:$j^{12}$
Simplify: $j^{27}$
Determine the nature of the roots of each quadratic equation without solving it:$9 x^2+30 x+25=0$
Determine the nature of the roots of each quadratic equation without solving it: $3 x^2-2 x+4=0$
Solve each equation using the quadratic formula (when necessary, round results to three significant digits): $x^2-4 x+5=0$
Solve each equation using the quadratic formula (when necessary, round results to three significant digits): $5 x^2-6 x+4=0$
A solar-heated house has a rectangular heat collector with a length $1 \mathrm{ft}$ more than three times its width. The area of the collector is $21.25 \mathrm{ft}^2$. Find its length and width.
A rectangular opening is $15 \mathrm{in}$. wide and $26 \mathrm{in}$. long. (See Illustration 1.) A strip of constant width is to be removed from around the opening to increase the area to $672 \mathrm{in}^2$. How wide must the strip be?