Quadratic Equations (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

The solutions to the equation $x^2+gx+h=0$ are $\frac{1-\sqrt{17}}{2}$ and $\frac{1+\sqrt{17}}{2}$.

Find the value of $g$and the value of $h$.

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.