174 results for "root".

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• Question
This 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

Find roots and the area under a parabola

• Question

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

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

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

Given a randomised square root function select the possible ways of writing the domain of the function.

• Question

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 How-tos

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

Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by=0$. Complex roots.

• Question

Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''-by=0$. Distinct roots.

• Question

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

• Question

The derivative of  $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$. Find $g(x)$.

• Question

Find the roots of $\sin(z)=a$.

• Question

Differentiate

$\sqrt{a x^m+b})$

• Question

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

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

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

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

Solve for $x(t)$, $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$

• Exam (13 questions)

Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

• Question

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

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

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

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

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

Solve a quadratic equation by completing the square. The roots are not pretty!

• Question

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• Question

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• Question

Solve a quadratic equation by completing the square. The roots are not pretty!