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

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.

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.

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

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

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. 

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

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

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

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 $q(x)=0$.

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.

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

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.

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

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

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.

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.

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.

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

Find roots and the area under a parabola

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.

Find roots and the area under a parabola

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.

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.

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.

Indices and Roots: Questions based on Exercise Intro(b) from the Textbook "Engineering Maths through Applications" by Kuldeep Singh.

Intended for use as Homework Exercises.

Indices and Roots

Questions based on Exercise Intro(b) from the Textbook "Engineering Maths through Applications" by Kuldeep Singh.

Intended for use as Homework Exercises.

Indices and Roots

Questions based on Exercise Intro(b) from the Textbook "Engineering Maths through Applications" by Kuldeep Singh.

Intended for use as Homework Exercises.