Solve quadratic equations (non-simple case, two real, discrete roots) using the formula. Some, random, non integer roots.

Calculate discriminant of quadratic equations and use to determine number/nature of roots.

Calculation of quadratic discriminants.

State nature of roots.

Calculation of quadratic discriminants.

State nature of roots.

Calculation of quadratic discriminants.

State nature of roots.

Questions asking for the factoring of simple case (a=1)

Then using factors to find roots.

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

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.

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 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.

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.

A simple question to find the roots of a quadratic. Using to test integration of NUmbas into Canvas.

Given vector $\boldsymbol{v}$  find the norm. Since putting in square roots is tricky, actually input the square norm, so it's an integer.

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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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.

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

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

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

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!

Simple questions on square numbers, square roots, cube number, cube roots and prime numbers.

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.

Express $\displaystyle \frac{a}{x + b} + \frac{cx+d}{x^2 +px+ q}$ as an algebraic single fraction over a common denominator. 

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

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

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

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.