**Question 1:**Solve the following quadratic equations by factorisation.

$\begin{array}{l}\text{(a)}{x}^{2}-5x-10=-4\\ \text{(b)}3-x-2{x}^{2}=0\\ \text{(c)}11a=2{a}^{2}+12\\ \text{(d)}\frac{2x+7}{3x-2}=x\end{array}$

*Solution*:

**Question 2:**Solve the following quadratic equations by completing the square.

$\begin{array}{l}\text{(a)}5{x}^{2}+10x-3=0\\ \text{(b)}2{x}^{2}-5x-6=0\end{array}$

*Solution*:

**Question 3:**Solve the following quadratic equations by using quadratic formula. Give your answer in four significant figures.

$\begin{array}{l}\text{(a)}(x+1)(x-5)=15\\ \text{(b)}\frac{{x}^{2}+3x-2}{{x}^{2}-x-1}=3\end{array}$

*Solution*:

**Question 4:**If the roots of $2{x}^{2}+4x-1=0\text{are}\alpha \text{and}\beta \text{,}$ find the equations whose roots are

$\begin{array}{l}\text{(a)}{\alpha}^{2},{\beta}^{2}\\ \text{(b)}\alpha -\beta ,\beta -\alpha \end{array}$

*Solution*:

**Question 5:**Write and simplify the equation whose roots are double the roots of $3{x}^{2}-5x-1=0$ , without solving the given equation.

*Solution*: