Solve the following quadratic equations using technology:
Solve the following quadratic equations using technology:
Solve the following equations by using technology. Round your answers to one decimal place where necessary.
3 x^{2} - x - 10 = 0
x^{2} + 2 x - \dfrac{21}{4} = 0
4.6 x^{2} + 7.3 x - 3.7 = 0
Consider the equation 3 x^{2} = 6.
Solve the equation by using technology, giving your answers in exact form.
Give the solutions as decimals rounded to the nearest tenth.
Consider the equation 0 = - x^{2} + 2 x-1. Use technology to solve the equation for x.
Write down how many solutions the equation has.
Hence, state how many x-intercepts there are on the graph of the function
y = - x^{2} + 2 x-1Solve \left( 5 x^{2} + 13 x + 6\right) \left( 2 x^{2} + 13 x + 20\right) = 0 using technology.
Solve the following power equations using technology:
Solve the following power equations using technology:
Solve the following polynomial equations using technology:
Solve the following polynomial equations using technology:
The Widget and Trinket Emporium has released the forecast of its revenue over then next year. The revenue R (in dollars) at any point in time t (in months) is described by the equation R = - \left(t - 12\right)^{2} + 4. Solve the equation - \left(t - 12\right)^{2} + 4 = 0 using technology to find the times at which the revenue will be zero.
Neville needs a sheet of paper x \text{ cm} by 13\text{ cm} for an origami giraffe. The local origami supply store only sells square sheets of paper.
The lower portion of the image shows the excess area A of paper that will be left after Neville cuts out the x \text{ cm} by 32 \text{ cm} piece. The excess area, in \text{cm}^2, is given by the equation A = x \left(x - 32\right).
Use technology to find the lengths, x, that will have an excess area equal to zero?
For what value of x will Neville be able to make an origami giraffe with the least amount of excess paper?
An interplanetary freight transport company has won a contract to supply the space station orbiting Mars. They will be shipping stackable containers, each carrying a fuel module and a water module, that must meet certain dimension restrictions.
The design engineers have produced a sketch for the modules and container, shown below. The sum of the heights of both modules equal to the height of the container.
Write an equation that equates the height of the container and the sum of the heights of the modules.
Find the possible values of x using technology.
Find the tallest possible height of the container. Give your answer to two decimal places.