Quadratic Equations (Cambridge (CIE) IGCSE Maths: Extended): Non-Calculator Questions

i) Write $x^2+8x-9$ in the form ${\left(x+k\right)}^2+h$.  

[2]

ii) Use your answer to part (i) to solve the equation $x^2+8x-9=0$.  

$x=$................... or $x=$................... [2]

Solve by factorisation $10r^2-23r+9=0$.    

$r$ = ................... or $r$ = ................... 

$x^2-12x+a={(x+b)}^2$  
Find the value of $a$ and the value of $b$.  

$a$ = ...............................................
$b$ = ...............................................

The solutions of the equation $x^2+bx+c=0$ are $\frac{-7+\sqrt{61}}{2}$ and $\frac{-7-\sqrt{61}}{2}.$  
Find the value of $b$ and the value of $c$.  

$b=$ ................................................  

$c=$ ................................................  

  The difference between the areas of the two rectangles is 62 cm².

i) Show that $x^2+2x-63=0.$  

[3]

ii) Factorise $x^2+2x-63.$  

[2]

iii) Solve the equation $x^2+2x-63=0$ to find the difference between the perimeters of the two rectangles.  

.............................................. cm [2]

The lengths of the sides are in centimetres.
The area of triangle T₁ is equal to the area of triangle T₂.
Work out the value of x, giving your answer in the form $a+\sqrt{b}$ where a and b are integers.

The area of the square above is $30{\mathrm{cm}}^2$.

Show that $x^2+10x=5$

Show that the values of $x$ can be written in the form $a+\sqrt{b}$, where $a$ and $b$ are integers.