218 results for "root".
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Exam (3 questions) in .Algebra
Calculate discriminant of quadratic equations and use to determine number/nature of roots.
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Question in .Algebra
Calculation of quadratic discriminants.
State nature of roots.
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Question in .Algebra
Calculation of quadratic discriminants.
State nature of roots.
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Question in .Algebra
Calculation of quadratic discriminants.
State nature of roots.
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Question in .Algebra
Questions asking for the factoring of simple case (a=1)
Then using factors to find roots.
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Question in .Complex Numbers
Calculating the square root of a complex number using De Moivre.
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Question in .Complex Numbers
Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.
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Question in Ugur's workspace
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.
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Ugur's copy of Using the Quadratic Formula to Solve Equations of the Form $ax^2 +bx+c=0$ Ready to useQuestion in Ugur's workspace
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.
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Question in Ugur's workspace
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.
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Exam (1 question) in Conor's workspace
In this assignment, try and find the roots of a randomly generated polynomial, using the quadratic equation.
A test assignment to see if it integrates properly into Canvas. -
Question in Conor's workspace
A simple question to find the roots of a quadratic. Using to test integration of NUmbas into Canvas.
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Question in How-tos
The student is asked to find the square root of an integer of the form $\pm n^2$. If the root is not real, they should enter "nan".
A custom marking algorithm extends the built-in one to deal with "nan".
There's some custom javascript to set the expected answer correctly. In the future this will be possible in the marking algorithm - see https://github.com/numbas/Numbas/issues/856
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Question in Linear Algebra 1st year
Given vector $\boldsymbol{v}$ find the norm. Since putting in square roots is tricky, actually input the square norm, so it's an integer.
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Question in Linear Algebra 1st year
Given vector $\boldsymbol{v}$ find the norm. Since putting in square roots is tricky, actually input the square norm, so it's an integer.
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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.
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Question in DIAGNOSYS
No description given
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Question in Thomas's workspace
A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.
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Question in joshua's workspace
No description given
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Question in Differential Equations
Method of undermined coefficients:
Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$. (Equal roots example). Includes an interactive plot.
rebelmaths
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Question in Julie's workspace
Method of undermined coefficients:
Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$. (Equal roots example). Includes an interactive plot.
rebelmaths
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Question in Bill's workspace
Solve for $x(t)$, $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$
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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.
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Question in Engineering Statics
Find roots and the area under a parabola
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Question in Quadratic Equation
Solve a quadratic equation by completing the square. The roots are not pretty!
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Question in Content created by Newcastle University
Differentiate
\[ \sqrt{a x^m+b})\]
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Question in Rachel's workspace
Simple questions on square numbers, square roots, cube number, cube roots and prime numbers.
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Question in Bill's workspace
Find $p$ and $q$ such that $ax^2+bx+c = a(x+p)^2+q$.
Hence, or otherwise, find roots of $ax^2+bx+c=0$.
Includes a video which shows how to solve a quadratic by completing the square.
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Question in Bill's workspace
Express $\displaystyle \frac{a}{x + b} + \frac{cx+d}{x^2 +px+ q}$ as an algebraic single fraction over a common denominator.
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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.