Exam 14: Quadratic Equations

Determine if the roots of $x^{2}-21 x-2=6$ are real or nonreal, and whether they are equal or unequal.

A car is going at $20.0 \mathrm{~m} / \mathrm{s}$ . At the same time that it reaches the beginning of a kilometre-long track, it starts accelerating at $5.00 \mathrm{~m} / \mathrm{s}^{2}$ . How long does it take the car to go around the track once?

Write a quadratic equation that has roots $x=\sqrt{6}$ and $x=\sqrt{3}$ .

Solve for $x$ by completing the square: $2 x^{2}+x+1=0$

Solve for $x$ and $y: x+y=4$ $2 x^{2}+y^{2}=16$

Solve for $x$ in terms of $y: 2 x^{2}-3 x y-2 y^{2}=0$

Use the quadratic formula to solve for $x$ to three significant digits: $4 x^{2}-7 x+1=0$

Solve for $x$ by factoring: $x^{2}-11 x-60=0$

Use the quadratic formula to solve for $x$ to three significant digits: $2 x^{2}+3 x-5=0$

Solve for all real values of $x$ to three significant digits: $2 x^{6}-4 x^{3}+7=13$

Plot $y=6 x^{2}+1$ . Determine the coordinates of the vertex, the equation of the axis of symmetry, and the approximate values for the roots.

Solve this radical equation for $x$ and check: $\sqrt{x^{2}+9}-3=2$

A body is projected vertically upwards and moves so that $s=u t-16 t^{2}$ , where $s$ is the distance ( $\left.\mathrm{m}\right), t$ is the time $(\mathrm{s})$ , and $u$ is the initial velocity of the body $(\mathrm{m} / \mathrm{s})$ . Find the time it takes for a body to rise 275 metres, if its initial velocity is $150 \mathrm{~m} / \mathrm{s}$ .

Solve for $x$ by completing the square: $x^{2}-6 x-10=0$

Determine if the roots of $3 x^{2}-6 x+3=0$ are real or nonreal, and whether they are equal or unequal.

Use the quadratic formula to solve for $x$ to three significant digits: $10 x^{2}-15 x+2=0$

Solve this radical equation for $x$ and check: $\sqrt{x^{2}-3}=2 x+3$

Solve for $x$ by factoring: $3\left(x^{2}+4\right)+5 x=2 x^{2}+6(x+3)$

Solve for $x$ and $y: 2 x^{2}+y=8$ $x^{2}-y=7$

Solve for $x$ and $y: x^{2}+y^{2}=17$ $x-y=3$