174 results for "root".

Question in AJAY's workspaceThis is a new and easy way for solving quadratic equation. It is based on the property that the roots are equidistant from the average.

Question in Engineering Statics
Find roots and the area under a parabola

Question in Clare Differential Equations
Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$. (Equal roots example).

Question in MY QUESTIONS
Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots.

Question in All questions
Question is to calculate the area bounded by a cubic and the $x$axis. Requires finding the roots by solving a cubic equation. Calculator question

Question in MY QUESTIONS
Given a randomised square root function select the possible ways of writing the domain of the function.

Question in MATH6058 Engineering Maths 1
Factorise three quadratic equations of the form $x^2+bx+c$.
The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Question in Demos
Give the student three points lying on a quadratic, and ask them to find the roots.
Then ask them to find the equation of the quadratic, using their roots. Error in calculating the roots is carried forward.
Finally, ask them to find the midpoint of the roots (just for fun). Error is carried forward again.

Question in Howtos
This question asks the student to give a function with a particular root. It then asks them to divide by (x{root}), and uses adaptive marking to mark against the previous answer.
This uses the "expression" data type, which is currently undocumented and experimental.

Question in Content created by Newcastle University
Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by=0$. Complex roots.

Question in Content created by Newcastle University
Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''by=0$. Distinct roots.

Question in Content created by Newcastle University
Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

Question in Content created by Newcastle University
The derivative of $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$. Find $g(x)$.

Question in Content created by Newcastle University
Find the roots of $\sin(z)=a$.

Question in Content created by Newcastle University
Differentiate
\[ \sqrt{a x^m+b})\]

Question in Content created by Newcastle University
Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

Question in Content created by Newcastle University
Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots.

Question in Content created by Newcastle University
Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$. (Equal roots example).

Question in Content created by Newcastle University
Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

Question in Content created by Newcastle University
Solve for $x(t)$, $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$

Exam (13 questions) in Content created by Newcastle University
Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

Question in Content created by Newcastle University
Complete the square for a quadratic polynomial $q(x)$ by writing it in the form $a(x+b)^2+c$. Find both roots of the equation $q(x)=0$.

Question in Content created by Newcastle University
Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.
Entering the correct roots in any order is marked as correct. However, entering one correct and the other incorrect gives feedback stating that both are incorrect.

Question in Transition to university
Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Question in Transition to university
Factorise three quadratic equations of the form $x^2+bx+c$.
The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Question in Transition to university
Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Question in Transition to university
Solve a quadratic equation by completing the square. The roots are not pretty!

Question in NC PreCalculus
No description given

Question in NC PreCalculus
No description given

Question in Andrew's workspace
Solve a quadratic equation by completing the square. The roots are not pretty!